Presumably if the F/O learned to fly on a Cessna or Warrior he was qualified to set take off power himself. Why not on bigger aircraft? It is not exactly rocket science to push one, two or four throttles forward...
Not rocket science, the training focuses on take off aborts in the phase of changing hands since the captain is usually responsible for stops once the take off run has begun.
"Working in an airline that works its way out of boeings into airbii we used to have company SOPs in which only the captain was allowed to taxi, except in case of role reversal for training purposes."
What would be the training purposes? Unless you mean a command course?
FOs were hired and trained as captains in waiting, therefore they had to be able to take over if needed and role reversal was a legal way to do that. It used to be more common, nowadays its rarely done, could be that i'm just too lazy though after 15 years on the right side.
"Now that we adopt the full airbus SOPs [...] all FOs have to go through some taxi training in the simulator and two flights with a trainer before they will be allowed to taxi an aircraft, set take off power themselves and do the whole taxi in."
Would that training not happen automatically during the type-conversion from B737 to A320?
In the future it will, currently we still have company SOPs on the airbus which are centered around a silent cockpit concept. There's no FMA callouts and nearly no checklists (just before start, after start, parking and secure) as well as no normal FO taxying. The move to OEM SOPs is just a money saving venture, not because their SOPs are deemed better. And of course those of us who have flown the Airbus for the last 20 years have to be retrained to the new OEM SOPs as well, not only the newly airbus rated ex boeing guys.