I think it's a valid complaint. AA has been reserving more and more seats for elites. When I buy my flights - usually about a month out on elite-heavy routes - it's common for there to already be no seats for non-elites to select for free.

Certainly, if I had no seat assignment, I'd be wanting to get to the airport early. But stuff happens, and being checked in offers protections. If an unexpected traffic jam means airport arrival 29 minutes before departure, for example.

What AA should do: allow passengers with no seat assignment to check in online and get the same "priority verification" card that the ticket agent would print at the airport.

What the OP should do: Keep checking. Seat maps change frequently in the last 24 hours, as passengers change plans, standby or SDC for alternate flights, or get upgraded. And at some point, non-premium seats reserved for elites-only will get released to be selected for free by anyone. You can also set a seat alert with Expert Flyer (even the free version) to email you if one becomes selectable - though I'd still check manually every hour or so.