It was solved on paper. SpaceX did it.
Note, too, that nobody else was thinking about solving this problem in 2001. Or 2011. Space had become a jobs program per ArianeSpace and ULA.
What SpaceX did was to put a second stage on top of that, scale it up, and make it automatically guided. You're going to have a very, very hard time arguing that this is anywhere even near the level of innovation that NASA or the Soviet space program achieved in a third of the company's lifetime.
As for the stagnation in space, sure. That's the issue with government programs in our current paradigm, they are heavy and the best course of action is seldom taken. Also, for some reason the US has an aversion for SoEs, so NASA, for ideological reasons, wouldn't have been allowed to make their own reusable launch vehicle and make a profit out of it.
For example, the idea of reusable rockets with the first stage landing vertically actually originated at NASA in the 70s. It wasn't pursued because realizing it at the time would require a human to guide the descent, which makes it very impractical.
SpaceX applied modern tech to an old concept, a reusable first stage via powered landing. They didn't do that much innovation. Landing a booster was already a solved problem, now the matter was to scale it up and automate it.