If it takes 10,000 or 20,000 people on the ground to keep each person in orbit, you're obviously never going to put many people into orbit, and for each person in orbit someone has to pay the salary of all those people on the ground. The solution is to build rockets using less money and fewer employees instead of bloating the budget so the same inefficient system can just get "embiggified".
I agree with virtually everything you've said - and the point of this thread isn't to thump on NASA. Someone upthread just said that NASA seems under-funded relative to the Chinese and IMO they seem very well funded.
One thing that is encouraging is NASA subcontracts more of its services today and private contractors should in theory be more efficient so long as they are not simply trying to suck the public nipple.
In terms of a mission NASA seems, "lost in space," but I'm sure insiders in the agency would blame that on the White House. GW Bush wanting to go to the moon and Obama reversed course midstream with that objective to landing on an asteroid instead.
Perhaps the agency should be long term funded with a clear mission. Say what you will about the Chinese and their system of government, but when they make long term goals [and it isn't only in space but also infrastructure] they don't waiver when a new president enters office or the congress wants to shift focus.
edited to add:
If I were in charge of NASA I would make their sole mission to find any kind of life in space with proof. Such a find would be bigger than landing a man on the Moon as we did 40 years ago and as you say leave manned space flight moving forward to private industry.