For starters: please use punctuation. Those sentences are longer than the FFXIV:ARR maintenance durations.
Secondly: Why are you using low level dungeons as an example?
Thirdly: A good white mage won't -need- to save a tank from brink of death with proper techniques and vigilance, rather than eyeballing their HP bars - Remember when I mentioned about 90% of the white mages being bad?
Lastly: The scenario's you describe are strange. Raid wide damage + big hit on both tanks and only save one? A competent healer would wait healing the rest of the party and knows the tank has higher priority during that moment. Name an encounter where the entire group takes continuous damage while the tank(s) are both taking big hits at the same time. If it's an 8-player encounter, do include both their healer's roles and priorities.