The real answer here is that NASA simple doesn't have the flexibility. The 10x engineers you want should have existed in 1970, because that's where most of the technology was developed.
NASA was forced by congress to put together a large rocket with all existing technology and infrastructure, something they have not done since the 1970s. The last rocket they tried Ares 1 was maybe one of the worst rocket designs ever made and cost an absurd amount of money given its possibilities.
NASA is also hard locked into locations, the NASA Johnson Space Center is politically important and wanted the development. Are the best engineer in that location or in LA where SpaceX put its main engineering efforts.
> Or is this just a matter of a problem being hard to solve, even with the best engineers and the institutional knowledge that comes with decades of experience?
Its a hard to solve problem either way. Made harder by the history and constraints at NASA.
The more relevant question is, should you solve this problem? As Elon Musk often says, are you asking the right question?
That is why for profit rocket company have largely moved away from hydrogen and away from solid rockets.