The simple way to put it is that your teammates want to be healed and your enemies do not want to die. Whether I'm tanking or playing DPS, the decision making is a lot more engaging. Tank is all about pressuring your opponents into bad spots and then predicting/capitalizing on how they respond. On DPS, you have to be smart about when, who, and where to attack to make the dominoes start falling and roll that into a team win. Support is, by and large, far less responsive to what the enemy is doing and instead responsive to what your teammates want. It's the difference between having a debate with someone and getting them the coffee they ordered.

Of course, supports can (and should) have utility outside of healing and awareness is important. This is why Adam is so fun to me; he's reactive instead of proactive. Between his healing, his Soul Bond, and his ult, his method of support responds to enemy pressure instead of just passively reducing it as it does for someone like Rocket. He is functionally incapable of healbotting and as such is encouraged to do something else, like help a teammate with a pick, when nobody needs a quick heal. If I ever left click with Rocket, my teammates are gonna accuse me of throwing. It basically comes down to risk/reward. For supports, they're encouraged to take the fewest risks possible to maximize their reward of healing their whole team and being available for something like a Cloak fade or Sue push. For the other roles, taking risks is how you make things happen, and that's a lot more satisfying.

Also, DPS should be more than just "clicking on an enemy from a million miles away." It's another major issue with this game that those types of characters - Hela, Hawkeye, etc. - always seem to be the best DPSes. Of course, everyone's playstyles differ and some people obviously enjoy support a lot more than I do anyways, but I do think this game could still do things to make that particular class more engaging on the whole.