AAA (or insurance) is generally not directly providing the emergency road service. They are subcontracting out with a local company. This makes quality variable, depending on the specific company and/or specific driver. I expect the vast majority of subcontracted organizations are acceptable, but some are not. One can list anecdotal examples of both exceptionally good and exceptionally poor quality service with AAA (or insurance).
For example, one towing service AAA uses has almost entirely 1 star ratings by real customers on Yelp with comments about not arriving after waiting 3+ hours (common issue, mentioned in many reviews), drivers not speaking any English, damaging cars by dragging tires and wearing transmission with car in park when towing and/or hooking car improperly, charging tow driver’s meals to customer’s credit card, texting on phone while driving, driving female to deserted parking lot in tow truck then hitting on her, throwing away customer’s phone and breaking it after customer refused to pay extra and tried to call AAA to confirm no extra charges, and even stealing a towed car leading to police report being filed.
I haven’t experienced any of the above, but the towing services AAA uses in my area that I am familiar with all have far better reviews/comments from customers than the tow company described above. My only major issue with a AAA service call was the car damage from jack dropping I mentioned earlier. The local tow company affiliated with the tow driver handled the repair, which I expect would have cost thousands at an area body shop.