Throughput wise we’re honestly fine. I’ve healed a bunch of keys on 4 of the healers so far.
Does monk take more effort? Yes, by far.
Your point on mana however is spot on. I’m running oom faster than any of my co-healers in raid. And if I try to conserve mana I sit at the bottom of the meters by a large margin. I think something more is required to fix this rather than just make Mana Tea baseline.
Make >old< Mana Tea baseline. And instead of building stacks off Chi spent, have us build stacks off crit. Oh look, Mistweaver finally has a scaling stat. 
Have the base functionality work like the glyph did. Instant use 2 stacks, 15sec CD. 2% mana return per stack.