It is a matter of perfectly ordinary empirical fact that we live in a universe that, so far as we can tell, is translationally, temporally and rotationally invariant. There is absolutely nothing in Noether's theorem that forbids us from having theories that violate momentum, energy or angular momentum conservation if they happen to describe a universe that has aspects that violate those invariance conditions.
There have been theories that do so, like Dirac's weird large number thing. These are completely legitimate theories, and are entirely subject to absolutely ordinary observational, experimental and inferential verifiability (which is why we know Dirac's large number thing is likely false.)
My point isn't that there can't be theories without those properties nor that the universe necessarily has them (or not). Just that, if it doesn't, we couldn't verify it scientifically.
https://www.reddit.com/r/askscience/comments/1m43o0/if_noeth...
http://www.preposterousuniverse.com/blog/2010/02/22/energy-i...
I think we should teach a lot more things using the basic framework of "baloney detection": Use what you know to prove that this claim is either bogus or potentially true. Show your work.
Conversely, a violation of NT might indicate just such a fracture.
In order for us to have a scientifically verifiable theory, or at least a consequence of a theory that is scientifically verifiable, that theory/consequence must be invariant under translations in space, time and rotation. Otherwise there would be no repeatability of any related experiment.
As such, by Noether's theorem, that theory/consequence must conserve momentum, energy and angular momentum. At the very least.
So any theory that didn't conserve these quantities couldn't be scientifically verifiable. So it's sort of a tautology that scientific theories conserve these quantities.