I think your assumptions are all still valid. You need a point wherewhen you decide who gets to fly, prepare the airplane, etc. Low-cost airlines can allow passengers to check in a long time in advance because they know that, given the way their fares are structured, almost everybody will show up. Besides, they have extremely short turn-around times so they don't need and can't prepare the aircraft an hour or more in advance.
Note that easyjet almost does what you suggest: If you book less than X days before the flight, you get a boarding pass immediately with no obvious option to defer check-in. Legacy airlines have a lot of things to deal with (no-shows, connectionflexible fares allowing passengers to change their plans on short notice, connections, overbooking, upgrades, etc.) that would make such a solution much more difficult to implement.