If you want "natural market forces" to fill that gap, you're either going to have to pay a lot more, or (in typical GOP fashon) allow the private sector to ignore the rules and provide poor instruction and moderate cost for most and good instuction for high cost for a few.
Isn't this more or less what is happening now, under the localized public school systems? Wealthy districts provide good instruction at high cost, and poor ones provide poor instruction, at a lesser, but still high, cost.
I find it hard to believe that the costs of additional standardized testing are anywhere close to the additional educational spending.
I have a friend whose husband is on the Board of Education for a district in suburban New York. Their district was getting a federal grant to do a whole lot of unnecessary work reconfiguring the school buildings, when there was nothing really wrong with them the way they were. This is probably a perfect example of how billions of federal education dollars are being wasted on things that don't improve education one iota. This is the typical result whenever the federal government gets involved in anything.