Why don't most physics programs study the primary sources? In other words: Why don't they include Newton's Principia, Lagrange's Analytical Mechanics, etc., in the curricula?
Much of Physics is now far better understood than when it was first formulated. For example, if you wanted to learn Maxwell's equations you are far better off using a modern textbook than going back to Maxwell's original work. Likewise Einstein's General Relativity. You mention Newton, but he used a notation that would flummox most modern students.
There are exceptions, for example Dirac's book on quantum mechanics is widely regarded as a classic and valuable even for modern students. However, apart from these exceptions the original documents are of most interest to historians of science.
Because it's in Latin.
That is not the only reason though, just read for yourself a relative modern translation:
I personally think this is not a straightforward way to express a physical law. As an undergraduate I would have really disliked to read such a text, even if it is written by Newton himself. As our knowledge advances we can connect different areas of physics, these connections might have not been obvious at all at the time of their discovery. Compare this with the lecture from Feynman (can be found online) about the same law.
The reason is that this is too time-consuming. The old papers are very difficult to read, because they have suboptimal presentation. Newton's Principia is not written well for the purposes of teaching mechanics. It is designed to emulate Aristotle in scope and completeness (but with the advantage of being correct physics), and it is optimal for the goal it served historically, getting Aristotle out of physics. It's absurd latin and old-fasioned geometrical phrasing with Greek-style geometry is suboptimal for pedagogy and clarity. One needs to use coordinate geometry and vector components in a modern presentation, there is no advantage to the old style.
In order to assign the Principia, one needs a modern translation of all the ideas in it. This is not provided by any source. Such a translation would keep all the arguments, but rearrange the order and the phrasing to be in common language and using modern calculus and vector component notation. This is very simple to do for someone who knows any physics, and Chandrashekhar did something like this in his annotated Principia (this is a very nice and respectful presentation). But Chandrashekhar wasn't writing an introductory physics book, rather he was trying to place the Principia's monumental achievement in historical context, to let modern readers know exactly what Newton was doing.
But I think it is possible to assign the Principia as an elementary physics book, if the translation is authentic and modernized. It requires rewriting the whole thing from scratch, but without throwing away any of Newton's insights. These insights are mostly contained in the special problems he solves.
I tried to provide an example of how to do this for less difficult things. The oldest is Archimedes "The Method of Mechanical Theorems", and you can read the gloss on Wikipedia, under Archimedes' "The Method". Using modern calculus, you can explain what Archimedes is doing in two minutes, and you can see exactly why his paper is so laborious--- he didn't have an algebraic notation or a standardized way to talk about infinitesimals. One should do a similar thing for "on floating bodies", "the equilibrium of planes" (this is simple to do, since it is all center-of-mass results which are trivial with modern calculus), "on the sphere and cylinder" (also simple, but it requires summing the squares, which is simple with modern calculus of finite differences), and the other works. All physics comes from Archimedes originally, especially the concept of force and torque.
One of the ideas in "the method" is the observation that certain integrals involving boundaries which are curvilinear algebraic varieties end up being polynomials in certain plane slicings, and so give rational number integrals. The simplest example he gives is of two cylinders intersecting at right angles. The question of which figures enclose rational volumes has never been investigated again, as far as I know, although it is interesting. It is similar to the question of periods, but it is different because of the slicing freedom. If people are familiar with the method, maybe there is interesting mathematics left undiscovered here.
With Newton, people keep the statement of the three laws of motion (the least important part of the Principia) and throw away all the special problems Newton analyzes. This is exactly the opposite of what they should be doing. One can state Newton's laws today as follows:
That's it. That's Newton's three laws. There is a further result
If you add the assumption that all matter is composed of points with pairwise forces which are attractions and repulsions, you get Newton's model of the world. The division of the laws into "1st law" "2nd law" "3rd law" is arbitrary and unnecessary, and only of historical interest. If you start with these two assumptions, you can state the three laws and show why and how they work, and the angular momentum law, and how and why it works, and then you can go to the special problems.
Newton's argument using infinitesimal triangles that the angular momentum is conserved during a radial attraction/repulsion event is essential, and it needs to be preserved unchanged. Newton's argument about the parabolic shape of spinning water needs to be preserved, although one should use the notion of potential energy in the argument. Newton's derivation of the speed of sound needs to be transmitted with both a derivation of the wave equation and an explanation of the adiabatic/isothermal distinction. Newton's analysis of the orbits of the planets is a little difficult to translate--- Feynman attempted to do this in "The Lost Lecture", but this is a place where improvements are possible, because one wants to use the modern insights about the central force, while keeping Newton's insights about the inverse-square special case. I don't know how to best present this.
All these things are usually skipped in elementary books, and instead you get an endless stream of unimaginative problems that are copied from one book to the next. These can be summarized in about a dozen or two orthogonal mechanical problems.
Regarding Laplace, the issue here is that the method of secular perturbations is greatly clarified by using action angle variables, and some special transcendental functions which flip from angle to time. The presentation in Laplace (which I haven't read) is not going to be optimal.
Translating Maxwell is going to be a pain, because you need to keep the modern insight that E and B (and A and $\phi$) are fundamental, not E and H. Maxwell is mislead by the fact that it wasn't appreciated that electric fields come from point sources, while B fields come from currents, so he wants the continuity conditions across material boundaries to be the same for the electric and magnetic field, and this picks out E and H as analogous and fundamental. This disease infects the literature right up to the 1950s, it is only fixed in the 1960s (and Feynman and Landau and Lifschitz help here).
The insights in Maxwell are so enormous that it is impossible to describe what is lost. These are the material dielectric and magnetic properties that are described phenomenologically. In my opinion, a good translation of Maxwell is essential to keep the 19th century E&M thinking alive.
For thermodynamics the problem is more severe, because the original authors did not understand that entropy was statistical, and energy was fundamental. They thought that the energy was the fundamental thermodynamic function, not the entropy. Here, one can start with stat mech, explain the thermodynamic potentials, and then go back and translate all the old papers into modern notation. These are all enormous projects, however. Thermodynamics has not been transmitted well--- most of the old thinking is lost. Statistical mechanics has been transmitted well, and includes the old thinking in principle, but the intuitions are different. If you don't believe me, look at any 19th century physics journals where they are busy measuring the heat capacities of materials at different temperatures, nd there are dozens of annoying thermodynamic identities you have to internalize. There is no way that studying this nonsense is productive, but it needs to be translated to modern language. The chemistry departments are responsible for this, and I don't think they are doing a great job of this.
Regarding 20th century physics, it is essential to modernize the treatment of Bohr, so that old-quantum theory is preserved. This is done in a wonderful way by Ter-Haar in the 1950s in a little book called "Old quantum theory". The Wikipedia pages on Adiabatic Invariant, Correspondence principle, and Old quantum theory try to present the results in a modern translation, without fussing over the ambiguities that are now known to be caused by working to leading order in h-bar.
Some things missing from all modern books:
There are a bunch of other things that can be dispensed of quickly today, I can't think of them at this moment.
So the main reason is that the historical documents need to be modernized to be pedagogical, and nobody does this. The only person who (secretly) did this is Feynman! He would rework the results with incredible fidelity to the historical literature, but without saying he is doing history. Almost all his elementary textbook arguments are reworked forgotten results from the old literature, done in his own way. This is why they are such classics, in my opinion, they are extremely historically faithful.
It's because knowledge is being continually updated and errors corrected. Newton's Principia Mathematica doesn't even contain his second law where force is proportional to the rate of change of momentum. Lagranges's Analytical Mechanics is very difficult to follow where he used concepts such as "the living force" to represent $mv^2$ and levers and pulleys to justify his use of the principle of virtual work. Both these books can be summarised in a few pages without losing the basic principles of what they were doing.
Productive young people at the cutting edge of research are lead by their peers and modern textbooks. Please, please don't look at the old text books until you understand the modern ones, otherwise you'll end up on a merry go around in the past, convinced you've discovered something new.