The only real reason that all the manufacturers went to 24v is that they can run a lot lighter wiring, reduce weight, and presumably save money. It's a lot like when all the car manufacturers went to 12v from 6v systems. Except with so many older airplanes still on the line, there are many 12v models still very active. But if the systems are designed to run on 12v, they will run just fine. Of course, if your mechanic installed a 24v flap motor in a 12v airplane, for sure there would be a struggle to lower the flaps!
The upside to having a 12v airplane is that jumping it is easy--any car or truck built after about 1956 can be used. The downside is that sometimes a rampie will assume that a certain airplane is one voltage when it's actually the other. Not a big deal if a 12v APU is used to try to start a 24v airplane--it just won't turn over or turns over so sluggishly that you will immediately realize the problem. But if a 24v APU is used on a 12v system, it can fry things really quickly, but fortunately what fries is the master solenoid, and if everything else is turned off, that'll be the extent of the damage.
I had that exact experience, with the 231 Mooney I used to fly. I had taken the owner and his wife up to Riverton, thinking I would come right back to Laramie. Instead, they wanted to show me their ranch, so the airplane sat out on the line in really frigid weather well into the night. When they brought me back, it had been sitting for several hours and was cold soaked. When it wouldn't start, Ol' Dummy here should have had it pulled into a hangar or otherwise pre-heated, but instead I asked the rampie to use the APU. He assumed it was a 24v model, he didn't ask me and I didn't think to tell him. That master solenoid fried so quickly it would make your head swim! Fortunately, the FBO had a proper replacement available, their mechanic came out after hours and replaced it after first dragging the airplane inside, and by the time he was done, the airplane was warm enough that it started easily. The FBO accepted responsibility, although honestly I was as guilty as their employee was.
Lesson learned.
FWIW, I carry a set of aviation jumper cables in my airplane at all times, and I've had to use them twice in 10 years, plus an APU start (very carefully reminding the rampie that it was a 12v airplane!). With the current battery (AGM Concord), it's not been an issue, but with the old Gill, it became a problem long before it was time to replace the darned thing--just didn't have the cranking power if the engine was balky.
Cary