A quick note: Nerfing healing output would be about the same as increasing healing requirements (save that the latter is a bit more ambiguous, as it might mean increased damage intake without increasing players' eHP, which then means might mean decreased TTD), except in that it'd be a relative buff to non-Healers' heals. It'd therefore probably be no more likely than generally increased damage intake.
:: I've gone ahead and italicized "relative to their kits" to make this constraint more clear.
For tanks there's a few other things they could do, like having more bleeding tank busters which require healers to be aware of both the main and off-tank's health for a time, or have some boss auto-attacks do damage to both tanks simultaneously, or bring back the ability for bosses to crit their auto-attacks. I'd personally think it might be more engaging for tanks if had to swap more often rather than simply using Shirk/Provoke during or after a tank buster.
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Bleeding tank busters seem a simple but really smart direction to go in, at least with greater frequency, as they increase healing requirements with minimal increased stress or do-or-instantly-die moments.
It's worth noting that many bosses by now do AA damage to both tanks simultaneously.
Having bosses crit would kind of do the opposite of bleeds, as they decrease leniency while increasing potential healing waste. That's not necessarily an awful outcome; just figured I'd point it out.