A "Why Not?" Moment

Do the people in Row 1 pay for status? Is the information that there's no one in front of you more valuable than the information that there's no one behind you? (One of them has much more influence over what you can do with your feet!)

As usual, Southwest kicks everyone else's rear. I think it is common among other carriers that you have to be at the gate 20 minutes before departure or you risk giving up your seat. At Southwest, the plane probably isn't even at the gate 30 or 40 minutes before take-off, and at 20 minutes before take-off, they are probably just getting started on boarding. It's wonderfully Hayekian. Stop worrying about algorithms & let the masses do their thing, I say.
The recent change at Southwest on numbering the boarding passes was just so the passengers didn't have to queue up to ensure an early spot in their group. I highly doubt that Southwest could match their current efficiency with a pre-determined seating system. In fact, with their incredibly fast turnaround times at the gates, open seating is probably necessary for them to meet their daily schedules.

The thing with Southwest, though, is that the fast loading and turnaround time is at the expense of passenger's check-in time and effort. As a Southwest passenger there is an incentive to check-in early which means either spending extra effort to get that online boarding pass first, or arriving earlier at the check-in counter. Open plan seating makes boarding more efficient at the expense of less efficient (read: convenient) check-in for the individual passengers.

I'm flying much less these days, but I do remember US Airways doing this. Multiple zones, with Zone 1 and Zone 2 being their preferred customers, and Zone 3 starting at the back and working forward from there.

What really botches it up is the a-holes sitting in the back row who put their luggage in the overhead compartment over row 1. If it wasn't for people like them, we could have much more orderly boarding of the plane.

If I really wanted to board a six-seat-across plane as fast as possible, I would break people into 12 groups, and board them in this order:
- even numbered, seat F. They all march on in order, from back to front, and sit down. Takes as long as it takes for that many people to walk through a door.
- odd numbered, seat A. Same marching order as above.
- even numbered, seat E.
- odd numbered, seat B.
- etc. Is it too early to say "etc"? Hopefully you get the idea. No one is being blocked from their seat by the person in front of them.

We'd really need to somehow allow people who board the plane last to still have as much of a shot at overhead space, though.

United boards status customers first (generally in the front), then all window, then all middle, then all aisle. This actually has a lot of academic support.

Back to front boarding is actually slower than random.

I say get rid of the overhead bins and you've solved 90% of the boarding problems regardless of boarding order.

In other words, the reason "why not" is that the solution, so intuitively attractive to you and David Friedman, is dead wrong.

Getting rid of overhead bins would slow down the end-to-end process by increasing congestion at baggage claim. If you normally have no checked baggage, you are slowed down a lot by needing to check and claim baggage. If you normally do check baggage, you gain a few minutes at boarding by not having to wait for people to put their bags up, but you lose time on deplaning -- you get to baggage claim sooner, but you usually get there before your bags anyway, and now your bags take longer to get there because half the bags that would have been in the overhead bins now hit the conveyer belt before your bag does.