My usual rant.
In 52 posts I counted 2 broken prop cables; how many hours were on them? Engine controls should be replaced at engine overhaul instead of being run to failure.
7 alternator failures, not including the regulator-related failure. Alternators should be opened and inspected every 500 hours (manufacturer recommendations) primarily to make sure the brushes aren't getting ready to fall out and make a mess of the slip rings and trash the whole alternator. Brush wear is the biggest single factor in alternator hassles. A broken alternator wire suggests that annual inspections are a little too casual.
5 Mag failures. Mags, according to their manufacturers, need to be opened and inspected every 500 hours (Slick) or 400 hours (Bendix). There are year limits, too. But they're too often being run until they quit, not a great philosophy for an airplane.
3 failed starters. Most older starters (like Prestolites) that use brushes are typically a 200-hour inspection item, and it can be done in a few minutes with the starter on the engine. The Bendix starter drives used on Lycomings have some very specific maintenance instructions, such as NEVER using oil on them, and cleaning them occasionally and lubricating with dry silicone spray, nothing else. Oil attracts dust, and soon the thing is getting bound up with sludge from the dust (and water, too, reacting with the oil) and it won't engage or won't retract.
In the flight school I had 7 airplanes that flew all over North America and seldom (very seldom) had a failure of any sort on those trips. Once the CO monitor indicated an exhaust leak; found a nearby shop that had a 172 muffler in stock and they sent the mechanic out to replace it. The students brought back the old muffler, and I pressure tested it and found nothing wrong with it at all. A flap control microswitch broke on another airplane and the flaps couldn't be retracted. Again, a shop a couple of hours away had one and replaced it.
I did all the recommended mag, alternator and vacuum pump inspections, and we paid close attention to everything on the airplane on inspections. Getting something fixed far from home is awesomely expensive, and it can tie both the students and the airplane up for days.
So, if you want to minimize the risk of an AOG situation, get that work done on your airplane.
I noticed a lot of tire failures. Details matter; I would want to know why they went flat. Were they trying to warn you by needing reinflating every week? Did hard braking spin the tire on the wheel and tear the tube stem out? Did you run the tire down to its cords? Was the tube a veteran of several tires? They don't last that long. Are the tires checking between the ribs? That lets water and sunlight at the cords and they start to degrade. If they fail, the tire blows out. Did you take off from a slushy runway and the slush froze the brake to the disc while in flight and the tire blew out on landing?
We only had one tire failure, and that was a hard-braking skid that ate though the tread and cords and blew the tube. Not my fault. An hour from home, too. I spent the school's money on replacing marginal tires; it was much cheaper than trying to get another 50 hours out of them and ending up with an AOG.