This has always bugged me about the standard pattern as it was taught
to me, especially the bit about first overflying the field, then
flying off at least a mile before descending to the 45. Why would you
leave the vicinity of a perfectly good airport, especially when your
engine is 60 years old? The FAA recommended approach makes perfectly
good sense from a collision-avoidance point of view, but it ignores
the fact that engines are not immortal.

It makes less sense from a collision avoidance point of view. Why would
you fly away from the airport into the path that incoming traffic would
take? That's just dumb.