This really is by design in FFXIV. Be it a deliberate thing or via poor development decisions.
Tanks can either generate excessive enmity, over mitigate stuff or DPS whereas a well played healer will always try to maximise their value from free and instant burst oGCDs and other high efficiency sources of healing such as Regen and the Fairy. This also leaves them with a lot of GCDs to either twiddle their thumbs or uh, DPS =(
IMHO the best way for SE to counter this would be to add more variety to the combos than just hate vs damage whilst also adding some depth to healers either via party buff or resource regeneration combos and such. Adding mitigation combos to tanks could perhaps be a decent stepping stone towards a more action mmorpg style that many hanker for.