I've had AAA for many years and would never be without it. I also have insurance w them on way too many vehicles. I just added RV coverage for my motorhome, that will quickly pay for itself if I ever need it. RVs by definition are road trip vehicles and they are not cheap to tow. I have 200 mile towing, Platinum Member or something.
To give an idea of how popular it is in SoCal, every year they call and offer me a free 2nd membership for a friend or family member. Last year, I called nearly everyone I know and could not find anyone who did not already have AAA!
The roadside service is awesome but it is lenient in some ways and strict in others. It's lenient in that you can loan your tows to anyone, it doesn't have to be your car that broke down or needs a battery, etc. They do have strict rules regarding certain tows, one of them is that I cannot go and buy a project car that doesn't run and have it towed home by them. I can't remember the others but it has to be actual roadside service, technically it's towing your disabled car to a repair shop but you can really have it towed anywhere.
I wasn't aware of the expired tabs rule but it sort of falls under the need for it to be a car you were driving that broke down. And flatbeds can absolutely haul unregistered cars around, in fact it's the only legal way to move one anywhere. I've done it or seen it done dozens of times in Los Angeles.