Would tanks be okay if SE swapped the damage between tank and healers?

[Somnolence]

So long as the fight ends by reducing the enemy's HP to 0, all contribution --no matter how indirect-- is ultimately via more quickly reducing the enemy's HP to 0 (even if through a bit more uptime via Expedient, a healer GCD saved, or whatever else). The primary way tank sustain contributes to rDPS outside of not needing to be rezzed is just... more healer offensive GCDs. But you can only push that sustain so far before it becomes redundant, failing to provide any difference to clear time or chance of success.

Why, then, would having excess sustain be in the tank's interest? And similarly, why would it be in the tank's interest to have higher maximum damage than healers, thereby reducing the relative value of proper use of sustain (rewarded through increased healer DPS)?

Excess sustain/utility is useful during prog, as it allows recovery in case healer dies/busy with rezzing and stabilizing somebody else/when having misplaced mits etc.

Sure when fight is optimized it might be so superfluous in that it does not save healers any GCDs, but it is still there just in case.

Good example of that is WAR Equilibrium.