This post should be renamed: Tanks want to TANK.

From what I read a lot of people complaining are people that don't/can't do savage and that's okay. Outside specific Tank mechanics in savage AOE (TEAMWORK MITIGATION) is fine. Tank bursters are usually tanks swaps or that far away that they can be mitigated with invuls. But it's still maximum 2 types (I don't recall any Eden savage having more than 1 kind of tank buster thought). Part of what's fun -to me- as a healer or tank is pre-fight planning and coordiante with my co-player on where to uses our oGCDs.
FFXIV currently have Team Mitigation coordination (Divine Veil, Sacred Soil, Virus) and Team DPS coordiantion (Trick,Divination, Etc.). Outside team mitigation tank ONLY worry about tank busters (-their own burst phase for "DPS stressors") and their respective tank mechanics (Like everybody else).

Something that might be too hard for casual content but might give a bit of thinking when tanking is to have (or bring back) several kinds of tankbusters for a single boss (Hard, Medium, Low damaging) this would make tanks more activily use their small CDs more often and not for mitigating auto attack damage (which is also good, you should mitigate as often as you can) it could even encourage to tank swap more often outside MUST SWAP or Invul tank busters.
Another small thing that might or might not work is to give a more visual reward to tanks that mitigate well, The Blackest Night is the best example you use it properly you get rewarded with a 0 cost mitigation skill (refunds mana), Paladin used to have that when he blocked something but it got removed. Making the "reward" fit with the job theme and identiy. (Pls square don't give TBN to all tanks).