I would seriously quibble with the anarchic independence you describe in #3 because (depending on the field certainly) you need to fund that work with grants and postdocs etc... Do you might feel like you can but it's generally largely dependent on convincing other groups to fund that work.
I'll Grant that The above doesn't really apply to pure math or philosophy
I'll admit that I managed to find a position with an abnormal degree of freedom in a fairly applied field (epidemiology) but I don't think that's any more atypical than people with particularly nice jobs in the private sector.
But right now, I'm working on projects in emerging infectious diseases, healthcare associated infections, some philosophy of science stuff, some algorithmic work in network science, and something that can best be described as "digital humanities".
I'll Grant that The above doesn't really apply to pure math or philosophy