Careful - you are now using conjecture rather than real statistics to back up your arguments. If engine failures on final are indeed 1 in a million then I should have been a Lottery winner by now.... I have either seen at first hand or heard from fellow pilots of this occurring at least 6 times over a 20 year period. It's happened to me once. Quite common in VW engined aircraft, A65s, C90s when despite carb heat they ice up.
The next statement is much more to do with pilots knowing how to hold their speeds and fly accurately down whatever angle glidepath they choose, so that they arrive at the correct landing point, at the correct speed & attitude, pointing in the correct direction, rounding out correctly & of course stopping in a straight line.
Saturday moprnings or indeed any other times are always entertaining at GA/light aircraft fields - people have to learn to fly you know, and they only learn by getting it wrong before they get it right (even when they are qualified).
Although I don't doubt your abilities, and have every respect & a high regard for your carrier experience, at least you had a hook to stop you!!!! (sorry, couldnt resist that). But even as a lowly PPL I can claim many more landings than that at a field with short runways close to a built up area.
Could I ask you something - would you adjust your rule if your home airfield's main runway approach was over a heavily built up area with no let out should your donk stop one day at 1.3 miles? One of our guys didnt. He was lucky when he landed on the sewage farm in nice new Cessna. He got out, but the plane was cut in two by the sewage sweeper rotor arm. His fuel guages showed quarter full of course so he knew his engine wouldnt stop.
Or would you be thinking about the traffic in front of and behind you (which may include anything from microlights to a fast twin) when you set yourself up on the base leg prior to turning finals? Lots of traffic, different speeds, a radio advisory service only and you have to start making lots of decisions to remain safe and considerate, not just sticking to what is best for yourself.