Germania, IIRC, tried that in the late 90s, offering a flat fare for every seat.
They had to roll it back very quickly because their bookings dropped unsustainably - nobody wanted to pay a fair price for a seat, even if it was cheaper than they might realistically have had to pay under dynamic pricing.
All that potential customers fixated on was that the flat fares were more expensive than the few cheap loss-leader seats advertised on rival airlines.
"The market can remain irrational longer than you can remain solvent" etc etc