Yes, cosmological principle is probably the most fundamental assumption in astronomy.
Most people don't realize that science—and even everything in life—has to start from some axioms/assumptions, just like math. I first realized this fact when I was reading the Relativity book written by Einstein himself, who challenges the assumptions in classical physics.
As time goes, some of the assumptions could be proved to be unnecessary or even wrong. There must be still some assumptions left, though—because without them, we can't talk about science, or anything, really.
Though it is worth noting if this were the case you would expect to see boundaries: if the laws of physics change due to spatial position, the discontinuity should produce an effect of some sort where matter and light transitions between regions.
Seems there are 2 ideas at odds. One is that the universe is infinite, in which case this is all localized and has no bearing on the universe outside of our small observable region. The other is that we are seeing enough of a bounded universe where the observations we make are of a significant enough chunk to make theories about it.
See https://en.wikipedia.org/wiki/Cosmological_principle
Basically, if this weren't to hold true, a lot of astronomy would fall over, even physics.