Seems like a tough argument for AA. When a passenger is deemed a late check-in, the passenger forfeits the confirmed space he paid for. Under fare rules, passenger can be charged a fare difference and change fee to travel on a later flight. Passenger forfeits any assigned seats he paid for, priority boarding, maybe some other benefits. A lot of forfeiture!
I suspect it turns out that a fair number of passengers historically checked in between 30 and 45 minutes before flight time. I know I often did. It may not sound like much, "just 15 minutes," but actually a crucial 15 minutes relative to passenger practices and expectations -- expectations, to be sure, formed over decades of the prior practice and also in light of UA and DL to this day largely (at most airports) still accepting 30-minute check-in for passengers with only carry-ons.