The consequences of your car's engine dying on the highway at 70 miles an hour is that you have to pull off the road without power steering, which may be difficult but usually isn't fatal.

The consequences of your plane's engine dying is a power-off stall followed by gliding to the ground followed by a dead-stick landing on whatever reasonably flat and unoccupied piece of land you spot on the way down.

Even the Beetle fails to work one day in ten.  Most people aren't in their cars for more than an hour a day.  I don't think I'd want to try two or four dead stick landings while I was still qualifying for my pilot's license, which takes 40 hours of instruction.

So while I think it may be possible for a wizard to learn to fly an old plane, I don't see how a wizard safely could learn.