Diesel engines in particular, do not like being run under no load - it is far far better to have them switched off rather than running. Boat owners struggle with this when moored, as they can't charge their leisure batteries by just running the the engine without engaging the prop.
I don't know anyone with a stop/start engine that has ever complained to me about having to replace their battery sooner. Personally, I drive clunkers, and have never had to replace a battery on one of those, despite me turning off the engine whenever I can. I think modern batteries are pretty damn hardy.
Yeah. While the instantaneous power draw is absolutely colossal, the actual energy drained from a battery starting a (healthy!) engine is fairly minimal, and its replaced very quickly by the alternator once it's up and running. Stop/start engines also use the ECU to stop the engine at the right point in the compression cycle for it to fire immediately, without cranking, so there's even less drain. (Even pre-stop/start engines in cars with modern ECUs tend to leave them in a position where they fire almost immediately.)
What kills batteries is deep discharge cycles. Sipping a bit of juice to start an engine and replacing it quickly does almost nothing to reduce its lifespan.
I don't know anyone with a stop/start engine that has ever complained to me about having to replace their battery sooner. Personally, I drive clunkers, and have never had to replace a battery on one of those, despite me turning off the engine whenever I can. I think modern batteries are pretty damn hardy.