Are there any airlines that offer unlimited monthly or annual domestic flight tickets?

I found this. I don’t know what the fares are like. Many many many years ago I remember hearing about unlimited passes with American Airlines I think, but the passes were quite expensive. Some things to think about are if you wind up going standby a lot of flights are very full. If you are flying alone it might not be a big deal, if you are flying as a couple or family it might be more tricky. I don’t know if you wind up flying standby, I am just saying if that is part of the deal take that into consideration.

My friends who are consultants (who fly out every Monday or Sun. and fly back every Thursday night – to the same client site in the same city every week for 45+ weeks a year) still have to get a ticket for each and every flight.
I’ve heard of them pre-arranging all the flights for a set price by calling the airlines directly and pre-purchasing all at once for a discount, but the flights are still individually booked.

There are very small commuter airlines (known now as local service airlines) that do fly from very small regional airports—like I know of Penair that flights out of Islip, NY (Long Island) to Boston..and those airlines will sometimes provide a “commuter book” of tickets..where you buy a series of flights for a set price. That’s about as close as you’ll come (as far as I know in the mainland US) to “unlimited” commuter travel by air. (But..there is still a ticket per flight..)

And, fwiw, for my job I fly about 70% of my working time—essentially at least 2 weeks a month, recently it’s been 3 weeks out of 4 (and have some colleagues that fly even more than me) ..and I still have to buy my tickets one flight at a time even when I’m going to the same client site over & over.