It's funny that you mention Cure 3, as it's one of the only things WHM really has 'going for it' in 70 content these days, and there are times we lean on it. However, that's really only seen in harder content like savages (or like mentioned above, solo healing). There's hardly a reason to use Cure 3 in leveling and story content; people have to be doing a fair amount of things wrong to really warrant it, or you just feel like playing it extra safe with everyone's HP and have the MP to do so.
Story dungeons and trials only become difficult if people make it difficult. There are some that can be difficult to heal if the other healer takes a tumble off the cliff and can't be raised, some that can be more difficult if your tank decides he wants to eat 6-8 stacks of vulnerability, so on and so forth. If people play alright and generally do mechanics, you're really not gonna see any healing challenge in story content. This is part of why you won't really find a pressing NEED to hit Cure 3 most of the time.
You mention DPS, though, and personally it's not much more compelling on the other side of the two fences. AST has more to juggle with cards which was just made easier by reducing the cast time of their primary nuke, and Scholar has lost a lot of its former DoT management as well, now with 2 normal DoTs, a nuke, shadowflare, and a super expensive DoT that is meant to mirror holy usage but can be weaved in for more single target damage at the cost of heavy mana. You'll unlock Aero 3 soon but you're probably not gonna find it much more engaging - it just becomes rolling two DoTs and spamming Stone as far as single target goes. I wouldn't say any of the healers have super interesting DPS, but Scholar probably has the most going for it just for the decision on whether or not to weave in Miasma II for the MP cost - and if you find most of your time is spent on damage on WHM, that won't really change on the other healers. We all spend just as much time throwing rocks, stars, or poisonous math at our enemies.
Meanwhile lilies have been awful since inception, and most over on the healer forums will echo that sentiment with various reasons why. I know many WHMs simply disable the lily gauge from their UI. Mine's still up but it's not like it impacts what I do in any serious way ever. You may also enjoy the decision making of what to do with your Aetherflow charges (likewise with AST cards), so it very well may be worth giving SCH or AST a try.
Tetra really helps WHM's feel. It's a simple ability gained at 60, but it's something I sorely miss in synced content. I'd say WHM losing its old MP management necessity would contribute to it feeling boring for some people earlier on, too, as it was at least something to make conscious decisions about that isn't as needed anymore even before Thin Air and Assize simply due to nukes costing less than they used to and getting more ticks of Lucid Dreaming than we had from Shroud of Saints.