What are some obvious objections that would spring to your mind?

Edit: sorry, that was very abrupt! Nice to have your input. I would be interested to hear what you think would be problematic about the Idea.

It's inefficient in the case of a wholly-owned subsidiary to require company A's shareholders to hire lawyers, setup bank accounts, books, etc. for a separate company B which ultimately provides the same limited liability vis-a-vis third parties. Joint-ventures become tricky between corporations. Corporations can't hold potentially toxic assets. There are quite a few good ones. Interesting nonetheless.

Also as with all corporate law questions, <other jurisdiction> allows it, so we'll just go there instead.

I'm not sure I understand your first point. If a company can't own another company there's no such thing as a "wholly-owned subsidiary". If you buy a company they become the same company.

I'll try to stick to one thought at a time.

Also super unlikely, and only worth discussing except as a theoretical exercise. We just aren't undoing centuries of law. Same reason trusts are here to stay.