I think proof of work is also necessary, though it is a really tricky point and not everyone agrees. I totally agree with your other points.
Discussion
Oh, most definitely proof of work, yes, but I see that as an essential part of Bitcoin (and elaborated on at length in the white paper).
When ppl claim that early distribution is unfair, it's like saying everyone should have received a free airplane after the Wright Brothers made their first flight. No, the new technology had been shown to be viable and everyone could now 'mine' an airplane for themselves, by putting the work in. A fae from perfect analogy but the point is that when a new technology is invented to and shown viable, it's up to ppl to recognize its potential and put work in to build upon it. And those who do are rewarded for their insight but also for the opportunity cost they potentially risked.