The thing that has always bothered me while taking my QFT course was the seemingly arbitrary nature of Lagrangians. For the Klein Gordon equation we just wrote down the simplest Lorentz invariant object and then went from there. For the Dirac Lagrangian we constructed some Lorentz invariant objects (in a different representation) and added them together. My colleagues always rationalized the Lagrangians we would construct as "the simplest possible non-trivial expressions" that we could construct using some mathematical objects (Dirac Spinors, complex scalars, 4-vectors, etc.) but that just hasn't sat well with me. Is the fact that we are effectively guessing Lagrangians indicative of some lack of understanding of the true nature (or framework) of the universe? Could these Lagrangians just be emergent phenomena of more fundamental theories?
Is the fact that we are effectively guessing Lagrangians indicative of some lack of understanding of the true nature (or framework) of the universe?
I don't think we are guessing at Langrangians so much as weeding out the ones that don't work. The comments above say it better than I can, but as far as guessing goes, I think a fair assessment of, for example, Einstein's work in GR especially, demonstrated a fair amount of guessing, before he arrived at his final equation.
According to Hans Ohanian's book Einstein's Mistakes Einstein went through revision after revision, of both the structure and interpretation of the EFE, regularly telling his colleagues, to forget what I said two months ago, here's the newest version.
That guessing period has long been forgotten, in today's application and research using GR as an effective theory.
I cannot see that developing a Langrangian is any better or worse that guessing at the math underpinnings of any physical theory. After all, how much simpler could it be, bearing in mind what it describes?
I don't expect anybody, including yourself, thinks the Standard Model could be as straightforward as $F = ma $.
I am not trying to be glib here, I am just not sure what you expect instead of the equations currently in use.
If it's falsifiable, by later testing of the say, particle properties that emerge from it, and it cannot be simplified it further, then what more can we expect?
Could these Lagrangians just be emergent phenomena of more fundamental theories?
Now this is guessing, I am not sure that we will ever stop looking, or ever find, more fundamental theories but to turn this into a specific physics concept question rather than a personal opinion reply, I think you would need to be more specific.