In our airline on the F/O's sector there is a complete role reversal (i.e. engine start, taxy, take-off, etc...) with the exception that the Captain will take the thrust levers once take-off thrust is set up until V1, and that the Captain will park the aircraft on stands with a guidance system specifically aligned with the LHS (or of course whenever he/she sees fit).
This applies to the Airbus, Captains must taxy and park the Boeing
on all sectors as there is no RHS steering tiller.
I would be interested to know the views from FOs, does it bother you or could you simply not care as long as the T/O power is set?!
In our airline it's nothing to do with actually setting the t/o power as such, in an Airbus any fool can put the thrust levers in the FLEX or TOGA detent, and as F/Os we are trusted to do that on our takeoff. The reason for the Captain to have his hands on the thrust levers once thrust is set, as 411A alluded to, surrounds the stop / go decision which in our airline can only be made by the Captain unless he/she becomes incapacitated. The Captain will also take control for the stop, again with the exception of an incapacitation.
At some airlines operating the Airbus the F/O will keep his/her hands on the thrust levers up to V1 on the take-off, I believe BA is one such operator. Usually in these airlines either pilot can call stop before V1 on the t/o and PF will carry out the stop actions.
At other airlines F/Os cannot taxi even with a RHS steering tiller installed, which is a strange procedure IMO given that control needs to be handed over at relatively critical flight phases.
So in summary almost every airline does it slightly differently, for their own reasons.