Originally Posted by
Lohe
In 10man disc priests are good because they synergize well with other healers.
In 25man disc priests are good because of uncapped Divine Star/Halo. (to a large extent, at least)
Priests are not dead at all.
To answer the OPs question about assignments. Healing assignments are much less relevant these days than they used to be, especially in 10man because all healers will have to do all things. Assignments are mostly relevant when the group needs to split up so don't worry too much about it. I'm not sure when the last time I had a legit healing assignment for a boss fight (such as "you heal the tank, you heal the raid"). Heroic LK25 before the area buff went out of control probably.
Actually, that's not true, Chimaeron is probably the real answer. Point is, only very specific encounter mechanics warrant healing assignments and who you assign to what often has little to do with their class. You'd be much better off learning the strength of the different healer cooldowns so you can assign those.