I mean, Volt engine issues, except for maybe valve covers w/integrated PCV on the 1st gens (same crappy part as the Cruze), and EGR valves on 2nd gens, are super duper rare, and those issues aren't mechanical or related to the fact it start/stops. It doesn't just start it up cold and run it full blast, at least from what I can tell from the screen it spins it for a few seconds before starting, probably to build oil pressure, noticeable when cold, then it revs it up gently as needed. Once the engine is warmed up, it does rev up as fast as it needs to, like if merging on the highway in Hold mode or with 0 miles of EV range left. If you are using it in hybrid mode cruising along on the highway at constant speeds it just stays on at a fixed speed pretty much like a regular car.
Except for head gaskets on certain years, and oil consumption which has been an issue across the whole Toyota lineup, Priuses never really have engine issues. 2nd gen Ford Escape Hybrid taxis are still common in SF and they haven't made them since 2012. Overall, while I do think start/stop on traditional alternator/battery/starter vehicles isn't ideal, when it comes to hybrids, including plug-in hybrids, there's really no negative effects on the engine.