It’s actually a “user fee”. From the FAA’s website, “The Trust Fund provides the primary source of funding for FAA and receives revenues principally from a variety of excise taxes paid by users of the National Airspace System. The excise taxes are imposed on domestic passenger tickets, domestic flight segments, and international passenger arrivals and departures, and on purchases of air travel miles for frequent flyer and similar programs. In addition, taxes are imposed on air cargo waybills and aviation fuel purchases”.
So this money should go to only aviation and not get cominigled with the general funds.
I’m not sure how you expect user fees to not add a lot to airline ticket prices. The airlines are the biggest user of ATC and airport services, so they’re going to pay the most into the system. But you can bet they aren’t going to eat those costs themselves; they’re going to pass those costs directly onto their passengers (who are really the true “users” of the system).