They're a bit unconventional, but sure.
The first and most obvious is DnD. The healers are all dual purpose roles. Paladin and Cleric are both tank/healer hybrids, and the tanks are just DPS that happen to have high HP pools, since you have to make some sort of concession for rogues. Any other healer is a healer/DPS hybrid as well. Healing exists to either keep people on their feet after a hard turn, or to prevent a death. Both things only come up a handful of times per dungeon, as healing in between fights is a hell of a lot more sensible. It's better to just kill the thing than waste a turn or two undoing the damage the bads just did. One takes a lot more resources than the other, both in spell slots and in turns.
Another is most JRPGs. There's no such thing as a dedicated healer. Everyone has to fight, or else be relegated to the bench. It's always more economical to just kill the bad quickly with more DPS than to be forced to fight longer just because you're able to heal more.
A third is Monster Hunter. Over there, there's no specialized roles. Everyone's a DPS, tank, and self healer. Though some people do take a healer role, they still actively take part in the others as well. They just pull back a bit more often than others to keep others healthy. Maybe this is cheating though.
But Overwatch definitely isn't. At least back when I used to play that game, Lucio was by far the most popular healer. Ana was difficult to play, and Mercy was just plain boring. But Lucio, he could heal passively while doing actually fun stuff. In the end, I think most Mercy players were either forced into that position and played her despite not liking her, or didn't actually want to play a shooter and was content sitting in the back, avoiding interacting with the actual game as much as possible.
Obviously, they're not 100%, as there's always exceptions. Some people enjoy being a healbot. But the scarcity of them in games where it's particularly obvious that's how you're supposed to play is quite telling, especially in the endgame. I know that most beginner healers play that way even in FF, but that style tends to adapt to something more aggressive as the players get used to the role. I almost never see the heal-bot style in FF's endgame, and the reason is that it's a pretty boring style of play unless if the game is designed around it.
Healing is boring as contrary to popular belief, it's not very adaptive. There's not much more you can do than spam one or two buttons until everyone's at max HP or dead. The fact that there's almost no synergy between each of our healing abilities is quite telling. Everyone else gets a rotation, but healers? Just a grab bag of skills that each do their own thing.