I can't ever remember giving myself a safety brief before takeoff in a single. If the engine quits, the decision has been made for you. It gets pretty simple right after that. I'm only interested in maintaining the appropriate airspeed and if there's some runway left well that's great and if there's not, I'm aiming for the clearest bit of ground available.
This sounds like yet another example of instructors trying to ape 'airlines' but with no direct experience of it.
I remember being admonished once by an instructor for not using the pre-start checks. He told me, rather proudly it seemed, that they were longer than a 737's. I said "we're only flying a 210, ya kidding me aren't you?"
Unfortunately he wasn't.