Did you try getting a tow on your own?
My bet would be that this had a lot less to do with AAA and a lot more to do with how many tow trucks are available in your area. Tow truck coverage isn’t as good as it used to be.
I see this a fair amount in my line of work, unless a car is blocking roads the tows are just taking longer. I’m sure it’s region specific, but around here it seems like having tow coverage with your insurance gets you a tow faster than just being a private citizen making phone calls for a tow. Unless highway patrol is expediting your tow it’s not gonna be fast.
And depending on the random stuff, like time of day and how many tows have gone out in the last hour even the “expedited” tows can take a long time.
