I had a turbo diesel BMW with auto start/stop as a rental. It was unsettling at first, but it worked well. It started at the same idle level as when the engine stopped. That was in 2010, and it wasn’t a new feature that year. I think we would have heard of problems by now since Europe has been using it for so long.
I’d be more concerned about direct injection than start-stop.
I’ve read about Mini-Coopers that need their intake valves cleaned with an abrasive spray every 60k miles.