Legend had it Musk hired Mueller after meeting him and seeing a liquid biprop engine he was building in his garage. That sounds exactly like the type of person you describe. “I can’t do the cool shit I want to do at work because of forms/approvals so I’ll just do it myself at home”.
He set an implausible but interesting ’mission’ from early on. He set the culture of the company from the start such that the concept (borrowed from the tech world) of failing and iterating fast actually happened (rather than just being talked about in corporate presentations). He brought naive but effective ‘first principles’ thinking to many of the questions or problems which probably helped avoid the conservatism of ‘old space’. He brought enough money to start, but it was little enough that they had to be scrappy and lean for survival, which probably fed into the culture and built a great team further. And (by luck or judgment) he hired the right people, like Tom Mueller, who was already a rocket engineer, but was frustrated by his previous industry experience.
(And of course, back then he didn’t have the baggage he has now, which made these things easier to achieve.)
The reason NASA was doing that was because of risk aversion and lack of innovation!
The shuttle was shut down because NASA couldn’t afford another disaster like Columbia and there had been absolutely no meaningful progress to replace it .
Without spacex, that would still be the case , Dreamliner is still not done a demo flight and Boeing would have held NASA by the balls and renegotiated from fixed price to cost plus contract as they have been doing for decades.
SpaceX forced the hand by delivering on commercial crew (CCS)
The shuttle had bunch of older parts designed for other programs and was 30 years old in 2010.
SLS flies on engines that are decades old from shuttle era with no plan for new engines and still costs in multiple billions per launch !
If not for spaceX we would be cheering BO for successfully delivering the Vulcan engines and being proud of that as pinnacle of private space .
BO official Moro is step by step ferociously. They were always culturally tuned to be risk averse and careful
Mike Griffin https://en.wikipedia.org/wiki/Michael_D._Griffin
I have no claim to knowing what SpaceX's secret sauce is, because the problem I think you run into immediately is that any sort of logical explanation then bumps into issues like the ones I'm mentioning here.
[1] - https://en.wikipedia.org/wiki/Tom_Mueller