It is quite hard to stop a mechanically sound engine rotating. I have seen it done in a C152; you have to pitch up at about 45 degrees into a deep stall, obviously with the mixture shut right off, and eventually it stops turning.
Not something most pilots are going to do by accident
So, if an engine totally stops in anything resembling normal flight, it is likely to be seized solid and trying to start it is a waste of your time (and a waste of battery capacity). Especially if the stoppage was preceeded by mechanical noises etc.
I am sure the great majority of engine failures where the engine continues to rotate are either a) carb icing or b) lack of fuel. You know what to do about the 1st one, and you should know (despite some dodgy practices being taught in the UK PPL training scene) what to do about the 2nd one
There will always be time windows where an engine failure is going to mean a landing into something which is not a nice field. A fair number of airports are in that category, in addition to mountains, forests, etc. All you can do is minimise those windows. But statistics is
hugely in your favour here. I am completely un-bothered about flying straight over the Alps covered by cloud at FL180; it takes well under an hour to cross the whole lot, which is well under 1% of my annual time. That's a very good bet. But then I didn't get my engine assembled by some cowboy.
And for over-water, you carry a life raft.
A stationary prop creates less drag than a windmilling one. And a windmilling VP one creates a lot less drag if you pull the pitch full-coarse.