Ditto about first-time ESTAs, but last time we renewed our ETSAs, I'm pretty sure it said something like 'now you can use the automated kiosk on arrival'. On arrival at Miami, all 'visitors' were being directed into a long line by officials in uniform with guns and radios - so we did what we were told. I asked a tentative question about the kiosks which was rebuffed (ignored) so we stayed in the long line - enviously watching rows of under-used kiosks.
At the desk, I ventured to engage the immigration officer in conversation, which was remarkably successful! He confirmed that we could have used the kiosks, and asked who said we couldn't - a chap in a blue shirt, I said. Ah, he said, we have had a lot of problems with them. That was almost an hour in immigration and the same again queuing in the baggage hall to be checked by only 2 customs officers. Hence our concern at LAX - which proved to be unfounded.
Ref the bag drop, I think that is only if your bags are checked all the way through (which they should be) otherwise I guess it would be the standard checkin desk.
Ref the comments about it being AA's responsibility to get you out - that is only any use if the next flight has availability.