It's a raid of random people, if people don't know how to adjust to fix these situations on a personal level this is what happens.

Example: Knowing dps and tank split up often times on this fight because there's no "left or right first for alliance X"

Either adjust by telling your alliance to start on one tank, watch which one the dps go to, moan and groan at healers to heal you better, or play a tank with better invuln/personal healing(cough paladin) in this raid.

Those are the only likely ways to fix anything, if you can't trust others then work around them.

And of course, tanks aren't born leaders... just because they initiate a fight.