Astronomy

These days those assumptions are considered pretty fundamental

Nope. The reason why the FLRW model does not include modelling boundaries is because it is very hard to model boundaries, not because they are unlikely.

https://en.wikipedia.org/wiki/Shape_of_the_universe

[Many finite mathematical spaces, e.g., a disc, have an edge or boundary. Spaces that have an edge are difficult to treat, both conceptually and mathematically. Namely, it is very difficult to state what would happen at the edge of such a universe. For this reason, spaces that have an edge are typically excluded from consideration.]

Conclusion: The primary reason why an apparent "flat" universe could still have boundaries is because the FLRW model is either incomplete or possibly even not the right model.

meaning one random chunk of space (the actual stuff of space, not like looking at stars and other structures of the universe) should be indistinguishable from another.

It also makes no sense to invoke the cosmological principal to "prove" there are no boundaries. The philosophical cosmological principal simply says that since we don't see boundaries they must not exist anywhere. That makes no sense because we would expect any boundaries to only exist in a very small percent of the total volume of space.