I don't know if the cat itself drove Quantum Theory forward much, although it does serve to show some of the weirdness of what is going on. That said, I'm not convinced it's as weird as all that. Basically:
1. Measuring a quantum system doesn't contain any statement of who carries out that measurement.
2. Therefore there is no reason why the cat can't measure itself.
Then it's a question of where in the great chain of who knows what you decide to sit:
-- The cat knows it is alive or dead at the end of an experiment, so it is one or the other and not both.
-- The man outside the box doesn't know, so has no choice[i but to regard the cat as being both alive and dead at the same time.
-- The man outside the room doesn't know what the man in the room observed, so has to regard the man has having both seen the cat dead and alive.
-- And so on...
I don't think this means that the cat [i]is] both, but as long as the next observer up hasn't carried out a measurement (looked at the cat, or asked the man who looked at it), then in describing the Quantum system you have to treat it as a "sum" of both options.
Looking at it this way all that is going on, really, is that "Quantum Mechanics is probability in nature".