Up until a few weeks ago I was a healer in my raid, as well as the raid and guild leader. We lost a dps and we had another good pally healer we could bring up (I was a pally healer) so I switched to my hunter and we brought him up. Now, when I was healing, it was me a holy pally, a resto druid and resto shaman. We NEVER had healing assignments other than I focused more on the tanks, and they focused more on everyone else, but everyone still healed everyone too. Now the new pally insists that they need to have assignments to the effect of "you heal the melee, you only heal ranged, etc." I disagree. I feel that with larger health pools resulting in less overhealing, such specific assignments are just counter productive, and result in people letting raiders die because they are "not their assignment". Thoughts?
I think assignments are needed for certain fights (Heroic Will comes to mind). In that case each healer has a tank and both heal raid.
However, in a ten man setting, I think it is more "open". I generally let each healer have a tank then the 3rd helps out in terms of tank healing assignments, but even then that's just for fights where both tanks are tanking at the same time. As you stated, it can cause deaths if one healer misses their assignment. While they shouldn't miss their assignments, mistakes happen and that can be lessened if everyone is able to be healed by any healer as opposed to saying, "Okay, Healer A, you only healer the Hunter, Mage, and Druid and no one else."
In the long-run it can make healers stronger by making them more independent. The weaknesses will be shown and then they have to "step-up" or else the raid will fail. And then there are many implications with this scenario as well.
Generally, unless you are going for world firsts, loose assignments are okay in a ten man, but I don't feel that you should only be restricted to that certain assignment.
Healing assignments can make healing more efficient and can save those situations where, say, both tanks are low and all of you choose to heal the same one, leaving the other one dead... but I've never really used strict healing assignments in a 10man unless we were encountering issues keeping people up in certain fights. Usually it's more "my priority is Tank A, yours is Tank B" (but we both do both; priority is just who we each go for first if both are hurt) or "during Raidwide Damage Phase, you spam your aoe heals on the melee group, and I will on ranged group." We do plenty of crosshealing. But that's about as formal as we get, and really only on fights where it is a risk that we'll have deaths if we're not coordinated.
Strict assignments are not a good way to go, priorities as better, as Tziva mentioned.
You want to make people feel responsible for a task/target(s), but not totally remove their ability to triage people as needed or create efficiencies, as sometimes it takes 2 or more healers to prevent a death if peeps stand in fire, or it may be more efficient for healers to use their strengths in combination (i.e. a druid hotting a target with a de-buff while another direct heals as needed). Many classes are even designed this way, to perform multiple healing roles simultaneously.
For the most part I haven't seen a need for assignments in 10 man raiding with a few exceptions. My guild recently started working on the Wind Lord fight and we are 1 tanking it. As such the tank can take really spiky damage at times and it helps to have one healer dedicated to the tank with the other two (we 3 heal the fight) topping off the raid as well as helping with tank healing when there isn't any other damage to heal. But I would definitely say as long as you co-ordinate cooldowns, you don't need to do specific assignments on most fights.