Heh, I guess it's my fault for not asking the question clearly. Everyone is talking about what professions a tank should have, or what professions make the most money because of daily quests, etc. Forget that my constant player is a tank (it could have been DPS or a healer) and pretend that your alts can do all that daily stuff. Also pretend that you're not worried about maximising gear for that one player since everyones constant player may be different.

I'm asking which professions do you need when stuck inside a 5-man instance? Enchanting is good for the drops that noone needs. It would suck to have to vendor drops all the time because the alt that is the enchanter is not in the group. What else? There are mining nodes inside the instance that would be tough to pass up (if an alt is the miner and they're not there right now then you missed an easy node). Similar situations on skinning and herbaslism. Missing rare reciples/plans could happen if the constant player does not have those professions.