I mean, WAR is already kind of there.
If you think of Storm's Eye as their 30 sec DoT/Dia, Inner Release as their Presence of Mind, Orogeny/thesingletargetoneIforgetthenameof as their Assize, Overpower as their Holy, Fell Cleave/Decimate as their Afflatus Misery, and Storm's Path as their Glare, it's ALMOST the same thing as you're saying above and parallels WHM. It only has a 1-2 before Storm's Eye/Path, and a 1-2 DPS rotation, but also has no GCD heals (and all actual tanking abilities aren't GCDs), and WAR/WHM have about the same number of total Hotbar slots/buttons.
If you removed their 1-2 in their single target combo, their 1 or 2 in their AOE combo, and combined Decimate/Fell Cleave and Orogeny/X into one button instead of two, it's basically WHM in tanking form. Complete with the party healing.
...and honestly? I'd have no problem with that, I like WAR and WHM as they are right now. Though I think it'd be nice if we had more variation in healers. Like AST is kind of like GNB with the APM, but there's not really a healing equivalent to, say, PLD and DRK.