In my experience, they just get absorbed quickly and the label of “startup within a corporation” gets dropped, becoming so-and-so’s org/team

When I've heard of this kind of thing working it's almost always informal and not pushed down from upper management. That also makes it very fragile as losing a few key people means the "startup" just gets absorbed into the larger culture.

> Why can't anyone figure out how to make that work?

A "startup within a corporation" can never work because it's not legally a startup. You're still an employee of BigCo, so they can't grant you tons of shares for a penny so the culture will never be the same. And even if they manage to keep the group outside of most corporate politics, you're still ultimately employees so you'll be bound by HR and security policies because they have to.

The way to make it work which is fairly common is for the BigCo to fund a new startup which is a completely separate corporation and let it go its own way. If it fails let it fail or if it succeeds then they can acquihire it back in some future.