Why is the infinite preservation of information an essential assumption to be made when developing physics laws? First of all, my current knowledge consists of Physics 101 in public high school.
Regarding the idea of information not being destroyed, this makes complete sense to me.
The thing that doesn't quite make sense to me is why:

It's fundamental for all our laws of physics that information can never be lost.

As stated at 4:32 of this Kurzgesagt video.
Why is this?
 A: Here is an answer with two layers.
1) The root reasons are almost the same as the ones that led us to energy conservation (and other conservation laws that are not proved to be true, but instead elevated by us to be physical laws since they constitute the most succeeding set of principles in physics -- even "more serious" ways of expressing the conservation laws in physics (e.g. Noether's theorem) rely on the naïve observation that the laws of physics have symmetry). We ask our physical models to capture the reversibility that we find in our physical laws and this, in turn, comes back as an assertion that is named as conservation of information. After all, it is sensible for us to welcome such an assertion.
2)
It's embedded in our mathematical contexture of QM where the time evolution exposes reversibility. The physical transformations that lead from one state to another render information itself recoverable. Imagine any physical action (a known example is burning a book), in the theoretical sense run the time backwards for that action -- the physical procedure that hosts the action will be there, since the computation that carried out this physical action allows it to be so.
But then, if you go on and ask, "Why it is embedded in our mathematical contexture in the first place?", I will say that finding the essential base as you requested is somewhat a philosophical issue which should be touched upon here only by stating that associating 1), which reflects our demands, and 2), which reflects our mathematics, finally brings us to a stage in which we will find ourself start asking "Why?" indefinitely (Maybe it's a nice point to share this video by Feynman). Therefore, I hope you are satisfied at least with layer 1) or layer 2). 
A: Here is one answer I got from an expert, I will simplify by omitting the mathematical derivations. 
Asserting that information is a conserved quantity means that information does not just pop into our world by magic, all by itself and out of nowhere. If we then assert that information tells us a story about things that have happened, conserving information then means that stuff does not happen all on its own- at least in the sense that macroscopic effects in our world do not pop into and out of existence or jump from place to place without causes that precede them.
From this we can go on to state that for everything that can happen, the sum of all the attendant probabilities must be 1. If it's greater than 1, I interpret that as analogous to the case in which a cause had two unrelated effects (you fired one bullet at a target and two adjacent targets got holes in them, as if you had fired twice); if it's less than 1 I interpret that as analogous to the case that a cause had no effect (you fired a bullet at a target and no hole at all appears, just as if you had not fired your gun). 
The conclusion is that conservation of information means that causes precede effects and specific causes produce specific effects. These are essential attributes of any model (i.e., set of laws) of the world we could choose to write down.
If you write down a set of laws which allow things to happen without cause or prevent things from happening with cause, then you are describing a world ruled by magic, not physics. 
As usual, I invite the experts here to weigh in with their own responses. 
A: Because quantity of information is closely related to entropy. If information were to decrease, then so could entropy and that would break the 2nd law of thermodynamics:

The second law of thermodynamics states that the total entropy of an
  isolated system can never decrease over time.

And according to wiki this principle is tied to many other things. The most fundamental one in my opinion is the "arrow of time", but I believe it deserves a lot of discussion.
