Space Shuttle wasn't cheaper. It was ridiculously expensive, with designs decisions that shouldn't be made in the first place. If it was just a rocket that launched astronauts into space. That would be one thing. It's quite another to carry literal deadweight into space.

Look at SpaceX's starship program. It's much more ambitious than anything we have on the drawing board. It isn't just another super heavy lift rocket, but a mass manufacturable reusable launch system. Everyone else is still thinking about how they will make reusuable rockets. Meanwhile, SpaceX is making their own game, playing on their own level.

Manned flight isn't a burden. It has nothing to do with why we stagnated in rocket development. In fact, manned flight is the point of SpaceX, especially colonization.