So my theory is a little different than most I'm seeing and reading. I don't think Kang is behind the TVA.

I think somehow Kang is manipulating the Fall of the TVA because they are the one thing standing between him and using time travel to attain power. You can't conquer the past if the TVA keeps showing up and pruning your new timelines.

He may not be manipulating it. Maybe the Fall of the TVA just opens up the possibility and we get a post-credits scene at the end of a former TVA agent picking up a Time Master style helmet from the rubble of the TVA, but somehow I think the fall of the TVA will open the door for Kang to become the conquerer.