The second tiller is an option on the 737, it is standard on the airbus (320/330 for us). We do fly both types and are currently changing to OEM procedures on the bus which includes (among a plethora of silly, unnecessary checklists and callouts) FOs taxiing the aircraft. On the boeing FOs cannot taxi the aircraft (except on fairly straight taxiways) as there is no second tiller.
Surprisingly, taxi training is done in the SIM for both CPTs and FOs and followed by one supervision sector for every captain and FO. Yes, most simulators are not really all that good at simulating, but new ones are much better, which is a blessing as taxi training is a requirement anyway for low vis operation.
All in all my airline thinks it quite normal to let FOs taxi the aircraft, even new hires that come from our flight school with around 80 hours of real aircraft experience and of course flying to the exact same limits as anybody else.
If FOs (and for that matter quite a few captains) are not up to the task, simply report them. I think it much unsafer to let them fly the same aircraft, take off and land them in all conditions if they are not even up to the task of taxiing said aircraft at a very slow speed (30kts is max for us) instead of trundling down the runway at up to 175kts.
Granted, personally i couldn't care less about taxiing the aircraft myself, im lazy like and rather just tell the captain where to go (commanding him on the ground...) and let him do all the work.