Suppose it's -46.1C and there are hundreds of people calling for a tow or boost. Yeah, it's going to be 24hrs, but they do triage the calls to get cars out of traffic and dangerous spots.
Thing is, CAA membership or not, you're going to wait. The difference is that the AAA service is prepaid by you.
I belong because I can get the Scoob towed 320km if I have to (never needed it, yes, my CAA dues/insurance are wasted) and for many discounts that we get. It's insurance, and personally, I'll pay the premiums to know that if I need a big rescue, it's there. A longer tow can cost 5+ years of dues, or more. We got a tow (someone else's car) that was $1300 and my CAA membership covered all but $100.
We save on hotels and other travel stuff all the time.