Airplanes are even more different.
Not generating power in a car climbing a hill makes sense because there is a very good chance that within a short period of time, you will be going back down a hill, and the driver will be requesting braking. You might as well put the energy in the battery instead of heat in the brakes. But in general, GA airplanes don't have brakes in flight.
If you don't run the alternator at take off, but then click it on 1,000' off the ground, you are still climbing, and there's no good data you'll be using the engine to slow down the plane anytime soon. So why does it matter if I run it at takeoff or 2 minutes later? I still need the same number of watts, and I can't grab those watts from somewhere they would have been wasted, so there's no fuel savings. You just get slightly better climb performance and then slightly slower cruise (or higher fuel flow in cruise).
In order to save fuel with an alternator in a plane, you need data that you are about to start a descent where the pilot actually wants *braking* out of the engine, and to shut off the alternator for a time before that event so you can then power the alternator in the descent. But this only works if the descent is a full zero power descent, not just a 40% power descent. In a car when you are on the brakes you are always at zero engine power. In a plane, much of our slowing down is just less engine power, not none.
The only other way I can think of to save power is to not run the alternator when the engine is ROP. If you have a power management technique that quickly gets you from takeoff to LOP ops, you might be able to do this. This would then mean you only steal energy from the engine at times that it is running most efficient. Given that most aircraft batteries only have 20-30 minutes of capacity to run much of a load, and you don't want to be discharging your battery deeply, you need to get from takeoff to LOP within a few minutes for this to be very functional.
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