Constantly spamming heals on parties that are near full HP is the hallmark of an inexperienced healer. Letting people fall low and using your tools judiciously is how you improve and become good at healing. Healing is a means, not an end. You can't heal enemies to death. Your party isn't more effective for sitting at full HP all the time. The concept works all the time, because groups rarely "get destroyed". Most content in games doesn't bring you anywhere near constantly scrambling to keep everyone alive. This is because skill gaps exist, and you can't tune every encounter to be maximally threatening.
My job as a healer is to assist my party in successfully completing encounters. Healing is one of the things required to do that. Uselessly spamming cure spells is not.
It's a concept for how support roles play that's at loggerheads with how actual gameplay works in nearly every RPG ever written. It's how bad healers proudly proclaim support roles play, because they insist on spamming the part of their kit that doesn't actually contribute toward ending encounters. It's the most narrow way of viewing healers. It's also the way the FF14 devs very clearly view healers, and we've all seen the stupid and boring design that's come of viewing healers as Cure spamming gasping waifus.It came from player fantasy. It's not some outer space virus. Some people saw heal/support healers somewhere like an anime or a videogame and thought it looked cool.
One of the major differences between healers and DPS is that most people in general have a more or less correct concept for what a skilled DPS looks like. You output as much damage as possible while avoiding taking damage and using your non-damage skills as needed to keep your party going. People (especially in FF14's community) have a bizarrely divided take on what a skilled healer looks like. The devs and lower-skilled players think good healers are Cure spammers that stop healing on rare occasion. People who actually know how to play support jobs well know that's total BS: you heal as LITTLE as possible while maximizing time spent doing things that are actually useful. But the other camp decries this as "bad healing", because you're spending less time on your "primary role". It's at odds with reality.