There is no legal requirement to show id or answer any questions to establish identification before flying. In other words there is no extra work required by law which the fee would cover.
Like someone who would deliberately show up to work in a speedo because "show me where in the employee handbook it says I must wear pants"
The TSA is literally doing all this extra work though, whether or not you think it's required by law. They're not just pocketing the $45 and then blindly waving you ahead.