The Administrator is appointed for a 5year term.

https://en.wikipedia.org/wiki/Federal_Aviation_Administratio...

Sure, taxpayers pay ultimately, but that's not the important part. The important part is that taxpayers currently don't care. They don't really have a stake in this. They are indifferent, because they don't feel the huge torrent of opportunity cost of a slow regulatory agency going down the drain. Pay for delay would make this visible. It'd immediately help to put pressure on politicians, and that will make the executive branch much much much more responsive to these issues.