> My car, for instance, turns off the engine when stopped, that can't be good for the engine and battery.

It's largely irrelevant.

More than half of the wear and tear in an engine happens during cold starts. Unless you're in utter gridlock, you won't experience them more often than when at the start of the trip.

Toyota's hybrids turn the engine off and on on a regular basis, even during cruising, and have a proven track record of reliability.