I think we're broadly in agreement. I too think it would be a waste to remove the party support elements of tank kits, there are times after all where the healer is preoccupied and someone's near death experience goes unnoticed, having a tank able to step in with cover/TBN/aurora/nascent flash (not healing the WAR as well because that's just stupid, SE) is good party design. Similarly having partywide mit OR shield OR heal (looking at you PLD/WAR) is also good party design and helpful to a healer without replacing them, I like good party interactions and if the tank wants to save me an oGCD or better a GCD then great, thank you.
My main problem with tanks though, as I said above is their self sustain more than their party sustain, and I don't want to remove that feeling of power or the agency that a tank has. I would be okay with Rampart being 30% mit plus 20% additional healing received if the content did enough damage to justify that, same thing with Guardian, I don't mind 40% mit plus some shield if there is some tank buster or something that validates it. So for me, weakening some things, particularly in the WAR healing department (someone suggested making things like Bloodwhetting's heal add shield HP instead and I think that could work, especially if it used a buff slot and had limited stacks similar to how Haima works) but more importantly increasing incoming damage by orders of magnitude to actually make the power that tanks and healers already have justifiable.
Further to the "it's not just tanks that are unduly powerful" argument, how often in 8-man content do you see a SCH or a SGE make their AST/WHM co-healer unnecessary? I see it all the time, I don't see it as a job design problem per se, I see it more as an encounter design problem, if you're going to have two tanks and two healers, all four of those players should be active participants, not two of them active and two on the bench waiting for their counterpart to screw up.