I would describe the purpose of healing as: filling up life bars to prevent death (and other consequences caused by missing hp). Fixing mistakes is definitely under the purview of healers. Some Dps may have some minor tools to heal themselves but they're are not anywhere near as powerful, available or quick. A lot of the time, healers are the only ones capable fixing a particular mistake

I think the only problem is the damage just isn't frequent enough or heals being too strong. There's a lot of time where the bosses just do auto attacks that aren't particularly dangerous and then the rare unavoidable aoe or stack mechanic every now and then. It certainly doesn't have to be to the point where healers are spending every cast on heals... The whole "spend all their time only healing" or "spend all their time only dpsing" is a false dichotomy.