It could be used, but it would greatly complicate a component that is otherwise very simple, not very efficient, and heavily stressed. Engine bay components get very hot indeed. It could be done with some difficulty with silicon parts, or perhaps less difficulty with GaN parts (or SiC if this were a high voltage system). Nevermind the commercial availability (currently ~boutique) and cost of packaging those devices (200°C+, usually gold and ceramic), of course.
In short, all you gain is slightly less heating in the winding -- reduced harmonic currents. Actually hmm, how much of that even is true, because, if the voltage ends up flat-topped, that's not instantly causing huge current spikes. The output impedance isn't nearly as low as a proper generator is. So that leaves slightly increased core heating due to the voltage harmonics, but that's really a small part of an already very toasty core -- due to the relatively high operating frequency and laminated iron construction.
Probably, significantly more efficiency would be saved through using thinner laminations, of higher quality material (lower losses, and maybe higher Bmax, though Bmax really only affects volts/turn at idle speeds), and tighter tolerances probably with a better salient-pole rotor configuration (as mentioned above). All of which increase the cost, for a low ranking system (that is to say, the electrical power in an average ICE vehicle is a tiny fraction of the total available power).
This would be applicable to hybrids and electrics, but I'm guessing they usually use direct-drive inverters, so regenerative braking, and generation from the APU where applicable, is trivial in the sense that the power train (both electrical and mechanical), is all there. (The control may be nontrivial, to get a controlled-power polyphase inverter system running, but that's just 1's and 0's; a solution exists, it's just engineering to find it.)
Tim