That is also a valid approach but I'm not sure it is more direct. Tax policy is generally only set once a year and only affects tax payers. Interest rates can be tweaked more frequently and (I think) directly impact a larger subset of economic players. That and the Fed doesn't determine tax rates.
Your point about how tax rates are set compared to interest rates is true, but could be changed.
I don't follow the second part though: pretty much everybody pays a significant amount of taxes, if only the likes of sales tax. Far fewer (though of course still many) players have substantial interest income or expenses.
