Southwest Airlines uses a system similar to the deli-system you're describing. Instead of seating passengers by rows as most airlines do, passengers are given numbered boarding passes which function like deli tickets. However, they do call people up in groups of 20-30.

Unfortunately, the system doesn't seem to dimish the tendency of passengers to cluster around the gate in mobs. It's a good idea, but not enough to work against the impatience of human nature.

I wasn't clear in my post. This is not to address the line for boarding (I have another solution for that).This is for the line at the gate counter (generally for people who want to check at the gate or change seats or fly standby etc.) Sometimes those lines get long.

One reason people might not like it is that when you're about to check in a ticket, you're often prety excited. Maybe most people wouldn't like the idea of rushing to the airport and then waiting casually in a line. Also, there would be a huge lag because those waiting could concievably have several large bags each, so when a number's been called, it might take a minute or more to haul all that luggage to be checked in. This would make people mad and maybe cut down on the airport's revenue, since people who are waiting would probably not shop while waiting, and the overall checking in experience would be longer and more stressful (since you'd be constantly worried that you somehow missed your number, and instead of having a deferred sandwich, this would result in not going to Mongolia like you'd always wanted).

Sorry, I meant "to wait casually in a lobby", not "line", as I'd written above.

Good luck!