Spirit Airlines actually has the right idea on this - you pay to bring an overhead bag aboard, and they mean business about it being the proper size. I'm able to get away with not checking a bag on the vast majority of my flights. I'm out of the airport like 5 minutes after I exit the plane.
Do you find that Spirit flights board and deplane faster? People struggling to get overhead bags when I'm feeling very cramped and just want to leave is one of my pet peeves.
It seems faster than average. There are aspects to their service that are horrible; their website, a la carte pricing and "buy your bags" terminology are incomprehensible if you aren't already accustomed to it. But they're cheap, quick and never even ordered any 737 Maxes.