You are more than welcome to become a prominent cosmologist and advocate for the term change.

"Inheritance" means very different things to programmers and normal people. You can't expect domain use to follow your sensibilities.

One is class¹ inheritance, the other one is (most likely about) wealth inheritance. They do, however, both respect the notion of inheritance, I don't see why anyone's sensibilities would be affected. But then comes "local universe", which although refers to the local part of THE universe, it drops the definitive article, only because coining a new (albeit controversial) term in astronomy is more rewarding for someone looking to leave a mark on the domain than to respect logic to a more sensible result.

¹ Let's leave for now what "class" means for programmers vs. other kinds of people.

In this case you literally gave a better example “class”, that said in cosmology there is only one universe ours.

The multiverse and other theories of multiple universes nominally belong to other fields of study.

Cosmology is the study of the universe we live in, specifically it’s development.

That’s why we have terms such as the local/near by universe and the observable universe. I find odd that none that that seem to take offense with the former mentions the latter, since grammatically they are identical.