Perhaps you should fly in situations you are not familiar with before you bang on about maths and single engine superiority.
Try 250 nm out into the North or South Atlantic (I've done both) in the dark and see how comfortable your maths makes you feel in a single instead of a twin.
Maybe sit in a hover against a mountainside in the dark and rain with 240' of winch cable and 2 pink bodies hung underneath you and see how comfortable you and your crew are with mathematical probabilities of engine failures in a single.
Perhaps IMC with a 200' cloudbase so you can get in on ILS or PAR with several important pax in the back - I'm sure your assertion that singles are at least as safe as twins will give great comfort.
Or North Sea with 15 bears in the back in shocking weather and a high sea state that would make ditching in a single (or anything else for that matter) very difficult.
"The relationship of weight/power/payload is key [to safety[in a helicopter]].
so where are your 3000 shp single gas turbines?