While having the text in the tabs is very useful to know what is under them, I don't think I've ever needed to actually copy the tab text. It would be a huge UX downgrade for me (and I think most people) if the tab text was selectable.
Some people might need it to be selectable for accessibility reasons and there should be a toggle for that, but I don't think "absolutely all text everywhere is selectable" is a good default.