I wasn't expecting them to supply a child seat. I wanted AWA to clarify their rule, which they did.

I bought AA tickets instead.

BTW, the reason I was considering AWA in the first place is because I'm arriving in DFW from ORD on UA at 11:45 AM. I want to leave DFW not too soon after arriving, but not too much later. When I was checking fares, the mid-afternoon flight on AA to LAX was almost double AWA (AA at other times, and other airlines, were the same as AWA).

Luckily, before I bought the AA ticket for a different flight, AA dropped the fare on my desired flight down to the usual level. So, now it's the same low fare, ideal time, with More Room Throughout Coach.