On the big pulls, e.g. snowcloak first area up till dogs, first packs in qarn till the door, pack in qarn around the pillar, or last room prior to kraken, I personally prefer if the healer does as little as possible to be fair. As it allows me to run through without worrying about the healer snagging off one or two mobs whilst I'm running. I'll position, drop some HP and hallowed ground as opener. Followed by sentinel + convalescence. At this point the healer can slowly get into healing. And with decent DPS aimed at making this a speedrun (e.g. 2x BLM) most trash is close to dead by then already anyway.

Most help of the healer in speedruns comes in form of DPS, not so much healing anyway.