My thoughts about AAA/roadside assistance: you're a mustachian and you keep your tires properly inflated and you replace them when the treads get low, right? You don't let your gas get too close to empty, because that's just a bad habit to get into, right? Your battery isn't 10 years old, right? Therefore, you'll probably only need roadside assistance around once every 2 years, and it'll probably only be a jump start. It's usually easy to find someone who has cables in their car, or is willing to jump you if you have the cables. Buying a battery and installing it is as simple as going to the nearest 24 hour Walmart and buying one.
My wife and I drive older cars and had "stuff" happen every now and then, but it's usually infrequent and we can take care of the issues ourselves. WORST case is that we have to pay for a tow 50-60 miles to the nearest metro area, because we get a flat and our spare tire is flat too. But what is that $50 bucks? $300 bucks? We're willing to take that financial chance for those one in a million scenarios.
As a AAA member and full-blooded Mustachian, this is one of those things where It Depends.
AAA has discounts at hotels and car rentals to the point where it pays for itself (we probably come out very slightly ahead) in our use case (GF travels a lot for work).
In addition, we both also drive out of town a lot. My last AAA call was when my previous car broke down (and turned out the engine was toast) in the middle of nowhere Michigan, on a Sunday afternoon, 150 miles from home, with a dog, right on the edge of cell phone coverage (calls baaarely worked with frequent drops, no functional data). The one before that was when a car blew a radiator hose on the highway on the way to the airport at 4am. Before that, GF's car finding itself with a three inch hole in the fuel tank (still don't know how that one happened, the shop it was towed to was really confused) and spewing out 18 gallons of gasoline onto I-94 on a Sunday afternoon 200 miles from home.
For us, it's worth the (slight and usually negative) cost for peace of mind (especially for GF when traveling long distances solo, which is usually at least once a month in her line of work). Shit happens, every few years, never at a convenient time, and I'm certainly not willing to buy cars that cost ten times as much to attempt to mitigate it. I do also have jumper cables and a booster, keep the tires inflated, replace tires/battery when it makes sense, keep the our cars maintained properly mechanically, and all that.