Sure, but I think this starts getting into ideology. I think people should be taxed rates that, in a vacuum, can be considered fair. I pay 15% of what I can, you pay 15% of what you can is about as fair as you can get. The reason I'm not fond of going beyond this is because you start getting into very subjective territory.
For instance while I agree with all you've said, excepting your conclusion, I'm sure you'd also agree that lower income individuals would also be much more likely to end up as the direct beneficiaries of where lots of government money goes to such medicaid/medicare and various social programs. Since these lower income individuals are going to be disproportionately more likely to utilize the benefits of these government programs, would it then not make more sense for them to shoulder a greater percent of the costs to account for this? I absolutely do not agree with this conclusion, but at the same time I also don't see any clear logical flaw in it.
So you can do an ideological tug of war, one way or the other, to no end on these issues. One ideology might have the wealthy give nearly all of their income away to help the rest of the population. The other end of ideology might have people give none away and rely entirely on market dynamics. I think a fixed and fair sum is one of the more reasonable ways to step outside of ideology and try to create a system that nobody really loves, but also nobody can create rational arguments suggesting is, in and of itself, unreasonably biased towards one group or another.