Since each class has it's "thing" that it's sort of expected to do, like fight monsters or bypass traps, it's natural for players to go "ah! you can heal us, that's your thing! do that!".
But healing is a thankless job. Most of your spells are woefully inefficient compared to anything else you could be doing. Much of the time, you're expected to save other players from their own lapses in judgement. Be it the Barbarian using Reckless Attack too much, or a dual-wielding Rogue bellying up to a powerful melee enemy.
"Oh it's fine, the Cleric will heal us!"
Except the Cleric will run out of spell slots fast that way, while many other classes can keep doing their thing all day long as long as they have hit points. And it's not very fun, either- even just using Healing Word every turn to pop up characters relegates you to nothing more interesting than cantrip spam.
Cure Wounds isn't even twice as good as Healing Word, and requires you to run up and touch a guy to heal him. It's just not a battle you can win.