Turbos are not new technology, they have been engineered to survive the stresses Ford, and other companies, put them through.
First, comparing them to diesels is out of the question lol. An average turbo diesel will run AT LEAST double the pressure of a turbo gasser. That is double the stress the turbo has to relieve every time it shuts off. They are also normally bigger in size and are not cooled in any meaningful way.
These turbos on our newer gas vehicles have great tech in them. They are water cooled, no uncontrolled heat characteristics are going to damage a stopped turbo impeller or housing. The bearings will keep oil inside as the turbo winds down during a start/stop cycle, which is only a second or two by the way. Sure, with the engine off there is little oil flow to the turbo, but there is also little flow out of the turbo as well, so oil stays trapped and lets the turbo wind down and start back up easily.
Let alone the fact that the auto S/S does not engage without a few met parameters, it is not going to engage if some part of the system is out of its comfort zone.
There is minor added wear to starter and batteries. The worst treatment you can give your starter and battery are cold starts. Hot starts are effortless for these parts.
At the end of the day, a turbo will become a wear item when you want a car going 150k+, especially depending on maintenance and use. However, maintain your vehicle and I suspect very few major issues will come from it.
As a side note I wish I was willing to cash in on people's ignorance like the guys who make **** like S/S disablers! $99 for a feature REMOVER that you don't even know the engineering behind. Hilarious. I wish.