Rich should pay more
The present fixed income tax rate can be changed any time within the usual constraints on the legislature just as a variable rate could be. With a fixed rate, the proportion of income left after the tax for lower incomes leaves even less left to pay bills. For higher incomes, there is plenty left to pay bills. The other problems you mention, which have been wrangled over for years, can't be allowed to stop enabling higher incomes to pay a fairer amount of tax.