WHY do we assume that the Universe for ALL observers is indeed homogeneous and isotropic????
Recently astronomers/astrophysicists HAVE plotted the irregularities and asymmetries of the residual Big-Bang background radiation and the "Bubble/Cellular", foamy, non-homogeneous overall nature of the observable cosmos ---- as seen from Earth's position. Will this not also look different from a different vantage point?
It all depends on what scale you consider. On scales smaller than a few hundred million light-years, you can have some pretty significant inhomogeneities. But observations show that the universe is homogenous on scales larger than that. That is, compare any two slices of the sky that are a few hundred million light-years across, and they'll look pretty much the same.
How can the universe look the same on large scales, but not on small scales? It's actually pretty easy to think of some everyday examples that mimic this behavior. Imagine that you're in an airplane flying high above the desert. If you're up high enough, you might not be able to see any features on the ground. But if you were to fly much lower, you might see elaborate features in the landscape. So whether one patch of desert looks like another patch of desert depends on what scale you're considering--just like the universe.