Assuming all Bitcoins had been discovered and fees were paid in US dollars (please ignore the obvious problems), what would an appropriate fee be? Would it depend on the size of the transaction? How would it scale?
Instead of asking what would be the fees if they were paid in US dollars, I think you meant to ask "what will be the purchasing power of the transaction fees, measured in today's US dollars".
There's some discussion of this at How much will transaction fees eventually be? but the short answer is that nobody knows. Left to their own devices the fees will be close to 0, which is a problem. No consensus has been achieved on how to fix the problem. Personally I think the goal should be fees on the order of 0.1% + 1 cent.