Did people not watch the videos of what to expect? Is crowd control even being used?
In Burning Crusade we spammed dungeons to get our healing sets to prepare us for heroics and then for Karazhan and onward. I remember spending days and weeks and months progressing into Karazhan until our group was geared enough to faceroll it in three hours and move onto Zul'Aman.
In Wrath of the Lich King we went into Naxx in blues and would down a boss or two per night until weeks/months later, again, we could glide through it in three hours.
We're only one week in. Virtually nobody is "geared." People are going to need to use crowd control to get through instances. They're going to have to learn how to actually think and plan their fights.
We all asked for this! We didn't want to see "free epics" for "noobs," "casuals," etc.
We wanted our epics to show for something. From what I am seeing the people that were prepared for this are getting it done and having fun. The people that are using crowd control are getting it done and having fun. If you treat this as tank and spank like Wrath of the Lich King then I guess we count down the days before you hit the "cancel subscription" button.
Your group needs to learn to work together and to play smart.
Yes, healing will be a challenge. But keep gearing up, learning the fights, and planning each step and you'll get it done. You'll get that sense of accomplishment and satisfaction. It'll happen. We're only a week in.