Maybe, I don't know. Sprit Airlines closing up abruptly like it did may refute your premise. They were the cheapest of the cheap, people hated them and now they are gone.
ULCCs thrive when they can maximize their time in the sky across as many different flights as possible. Filling up the day with many different flights allows them to rake in checked-baggage fees, reserved seat fees etc more often than longer mainline carrier flights. All of this went out the window when a large portion of their A320 fleet was grounded because of the P&W engine issues. This absolutely killed their utilization percentage.
Spirit died way more because of business management than it did because customers didn't choose on price.