For example, all 737 one engine out landings are made with Flap 15
Not true. The one engine inoperative landing checklist has a decision tree at the beginning which says:
1 Choose one:
- Landung using flaps 30 (if performance allows): Use flaps 30 and Vref 30 for landing and flaps 15 for go-around. Go to step 4.
- Landing using flaps 15: Go to step 2.
Step 2 then points to Vref 15 or Vref ICE which is Vref 15+10, step 4 just continoues with the normal flow at Use engine anti-ice on the operating engine only. Of course a note within the flaps 15 part of the checklist advises that autoland is not authorized.