For almost every part of the OP I agree that you just buy cheapest gas available. Though, if on a lease, I do try to at least find good gas but even though we have high end vehicles, Range Rover, BMW, I am not doing super in them when leasing. If I have a vehicle that I have purchased, I do use premium gas and good rating.
Rentals...haha sorry but if I could piss in them, I would.
As for the performance, I am rarely over 90 and I don't race anyone from a light, so, that is not my reason ever. Engine knock and just smoother running...maybe help with years 5-10...that is more my reason.
And I have never had a dealership analyze my fuel on any warranty issues. Would be almost 100% impossible to ever pin that on you anyway. What are they going to say - "You have inferior gas in the tank" if that ever happened to me, my response is..."who the F can trust those GS owners for what they put in my tank in NJ where we don't pump our own gas. I always ask for premium" and what would they do if it is a cert pre-owned and still on warranty? You didn't even own the car for the first 3 years.