You can't turn it off in the EU. The configuration is reset as soon as you power off the car. Considering this, assuming your claim is true, there should be vast amounts of damage to vehicles in the EU, which there isn't. In other words, the stop-start system causing significant damage is just one of the many myths popular among motorists.
I happen to be one of the people who didn't like it until I got used to it. The reason is simple - if you'd been dependent on an unreliable car in the past, starting the engine is associated with all sorts of uncertainties. Starters in particular seem to be the part that fails the most often in pre-stop-start cars. With each start there's a chance something will go wrong. This then translates to a bit of anxiety every time you hear the engine start even in situations where the probability of failure is insignificant.
I should have mentioned that my experience with stop-start is only with manual transmission cars that start the engine upon touching the clutch, sometimes before it is in full contact and usually before I'm ready to release it. If I'm going for a fast start I start the engine preemptively by lightly touching and releasing the clutch.
The other commenter's frustration with automatic transmission vehicles that start the engine upon releasing the brake sounds valid to me, especially if there isn't a convenient way to start the engine preemptively.
I have used two cars with start/stop: Renault Megane and VW Polo. Both were diesels and had automatic transmission.
Both of them started the engine just before my foot leave the brake pedal. I think they sensed the rate I eased them and decided that I'm going to roll.
I also drive an automatic Focus as my daily driver which doesn't have start/stop and didn't have a noticeable difference in their driving experience during stops, TBH.
Maybe some cars have different implementations and algorithms. A brand had on demand stop IIRC. You pressed brake a little harder to command the car to stop the engine.
My cars are too old to have the start/stop system but I've experienced it in rental cars and my immediate reaction is that I don't like it - especially the lag between when you move your foot from the brake pedal to when the engine actually starts running.
It wasn't so bad with a manual transmission (~2016 Mini Cooper) as I often start to ease off of the brake pedal as I start to depress the clutch, so once it's time to give it some gas, the engine is probably running.
That lag felt extremely annoying and potentially dangerous in an automatic ~2018 Volvo S90 though. Maybe I move my feet faster than the average person, but if I quickly moved my foot from the brake to the gas, the car would just sit there for a split second ... wait for the engine to start ... and then start moving. I know it's a low probability, but I definitely felt as though that car would give me a lesser chance of a making a successful evasive maneuver if, say, I noticed an out-of-control vehicle hurtling towards me.
My newer car has features to help offset this, including brake assist or whatever fancy name they call the feature. Remove foot from brake pedal, engine starts. The key is that it stays in neutral and the brakes remain applied until you hit the gas. You just have to get in the habit of removing your foot from the brake that split second earlier so the engine is running and ready when you want it.
This is how I feel about it as well, although if I think about how slow my current old car accelerates maybe it's not enough of a difference to matter.
If I understood it correctly, Mazda specially optimized its engines for this. They align the pistons during the stop, so they can start 2x faster (~0.5sec IIRC), so faster start, more comfort, less stress on the engine due to start & stop.
I think with the latest iterations, the damage part is not that definitive.
