I don’t think it’s pretty well established, there are cars that will happily stop and start the engine multiple times per minute, e.g. Toyota hybrids with their “HSD” drivetrain. It just requires some engineering.

It sounds like you're talking more about systems that supposedly disengage some cylinders while the car is cruising. Some engines with that kind of technology have been known to damage cylinders for multitude of reasons.

That's very different from the start/stop feature they're talking about. That's about fully stopping the engine when you come to a complete stop like at a red light and then automatically starting again when you get off the brake.

“While aggressive start cycles (>20 cycles per day) could lead to premature failure in the starter system of light- to medium-duty commercial fleet vehicles, modern fuel injection and engine control systems have eliminated any issues associated with drivers of typical light-duty vehicles turning the engine off while stationary for short periods and restarting the vehicles for <10 start events per day.” from https://publications.anl.gov/anlpubs/2015/05/115925.pdf

This paper seems to say that generally they aren’t a problem. I’ve only seen unsubstantiated claims that they are one.