How often do people lose the engine on final approach?
If you think about it logically, why is it more likely to die at that point than any other?
Most engines go pop when under load, on final approach there isn't a lot of load, so if you had no indications of problems before hand, why would it fail then? Apart from sod's law and carb icing.
Power changes usually cause issues as well as running at a high power setting for a prolonged period, but I've never seen any stats that show what regime of flight most failures happen in. It would be something I'd be very interested to see. Though I assume it to be in the cruise, since that is obviously where most engines spend their working life.
Going back to an earlier point.
If you retract flap, then you will lose lift and therefore height, use the K.I.S.S method for any emergency. i.e. don't start coming up with "cunning" plans when the doo-doo hits the fan, you'll only make it worse. Use the POH for procedures............ (repeat ad-nauseam)