I have CAA (Canadian version of AAA) and when I had a flat the other day, it was a frustrating process to get help.
For one, the CAA app doesn't have a bike option when selecting roadside assistance, despite the plan clearly offering services for cyclists.
When I called, they said that towing is the option available! I just needed my flat fixed, so I could go on about my day. I ended up asking my wife to bring me a tube, but it really left me second guessing my membership.
Hopefully, AAA is better.