In my mob (for some obscure reason which nobody will explain) the PF will set
the stby alt during climb and descent. On a line or sim check this point of SOP
is of course followed.
On an everyday line flight the captain usually sets it because its closer to him
and more practical than the FO having to do a bum's intrusive boarding-house
reach to get at it.
Slightly off topic but the PNF does the lights too - ever wonder why Bill Boeing
and even that Tooloose mob position the light switches overhead the captain?