That's not how it works. Car use an alternator instead of a generator because it lets them control how much electricity to make regardless of the speed at which the alternator spins. They basically vary the strength of the magnet in the alternator.
If they didn't the effect of "extra electricity" is a higher voltage, which would obviously be bad.
> I know cars waste a bunch of electricity (which is how hybrid batteries charge themselves when driving).
Hybrid batteries mostly save energy by capturing wasted energy when braking and when going downhill. Charging batteries from the engine makes the engine consume more gas.
Only for some workloads. A remarkable portion of the efficiency gain in hybrid vehicles is due to letting the ICE run at only the most efficient portion of the torque and power curves. In my experience (10 years in a Prius) regenerative braking is a distant second.
So when you brake your regular car you lose some heat to the environment, you don't 'waste a bunch of electricity'.
That you don't find a 'traditional' alternator in an electric or hybrid car is simply because the electric motor doubles in that role when required.
Almost all electric motors when spun will generate power, you'd have to do some work to get one not to generate power when driven.
Permanent magnet motors are the only motor that will generate power if you just pick one up and turn it by hand, and they are quite rare (and expensive) at scales larger than a RC toy motor
Absent any remaining magnetism you can 'flash' the motor core with a short DC pulse and then start rotating it with your chosen driver afterwards.
Just one sample (of many) of people using this trick for all kinds of interesting small RE applications: