I agree with the posters who say AA has no control over the hotels, but AA should certainly be monitoring these situations and stop contracting with these dumps. Although in my experience the only "free" hotel rooms I would turn down are in the DFW area.
We were put up at the Baymont in Grapevine and that place is an absolute disaster.
We wrote a letter as we usually do for trips to praise those who were very helpful in bad situations but also mentioned this.
I recommend the same here.