It's very simple, really. It's a combination of two facts:
The value of healing is capped.
Healers have a lot of spare time, a lot of spare resources and tools to do something with it.
For the first, just imagine healing would infinitely add overheal to your max HP. In such a case, even healing full HP targets would be useful. However, even then, once you pass the threshold where you can ignore all mechanics because you have more HP than being hit by all of them would subtract, healing more would be useless. The usefulness of healing is hard capped by the incoming damage.
Further, If a healer couldn't spare GCDs for not healing, people wouldn't ask them to do anything else because they can't. This has a lot to do with the power of healing spells - The faster you can get a healthbar from 1 to 100, the more time you have to dilly dally waiting for the next nuke to get them to 1 again.
If a healer didn't have the resources to do anything but healing, people wouldn't ask them to do anything else because they can't. You can probably imagine how hot people would be on Healers DPSing if every of their damage spells was Flare.
If a healer didn't have tools to use in downtime, people also wouldn't ask them to do anything else because it doesn't matter. But combined with the above it would mean excessive time of just doing nothing at all.
In short: Healers are too strong for the given content. That is on purpose, because SE wanted healing to be accessible, but it pretty much means that you'd need to constantly throw heavy hitting nukes at people they cannot avoid to make healers engaged for more than a couple seconds, because that's all it takes to get people back up. That is exactly what more difficult content does by the way - Double Whirlwind, Acid Raid, Double Mega Holy, Triple Cintamani, Akh Morn etc. And as soon as the barrage of spells stops... Healers go back to DPSing. Because they can.
And if that's already a thing in hard content, you can imagine that healers have even more free time and resources to spare on non-healing activities in casual content, as casual content has lower demands. That's what leads to people just jumping around idly. And if one person is jumping around idly and the other 3 are constantly doing stuff, it's not hard to understand why the 3 would like the fourth to do a bit more as well.
The unfortunate thing being that this "bit more" is only DPS, which people choosing a healer role often don't want to do. They often picked healer for the saviour fantasy, the samaritan, the good guardian angel that delivers people from pain, not to deliver pain themselves. That's something to respect, IMO, but if that is to come to pass, game design needs to support it. And getting that right is difficult.
Plus, no matter what you do, downtime will be a thing. You can only balance content for one set item level and one set skill level - people who are above that will experience varying degrees of downtime. So trying to fill the downtime with something that fulfills the healer fantasy is a thing to look into as well. But I'm just repeating myself by now.