Dungeon World is...

Dealing 10 hp to a character with 30 hps is a very different thing from dealing 10hp to a character with 5 hp. I've seen it done well, where it felt right and everyone was cool with it and I've seen it done poorly, where it felt like a let down that the character died. In both, the move followed logically from the fiction, but in one the danger was telegraphed and everyone knew how high the stakes were, while in the other it just seemed like a thing that happened.c

All right! All right! I get it already! It was a mistake to kill that bard!

I just played a Paladin last night (though we had a bard too) and didn't feel Lay On Hands was lacking.

A paladin worried about healing can also pick up Cleric spellcasting at second level, no problem.

Because it only results in a net gain for the party on a 10+, and the numbers are much less than what a clerical caster can heal, it doesn't feel like general purpose healing to me, more like emergency damage transfer.

That's exactly what it is. If your paladin wants to be a healer, consider taking Divine Favor at second level.

I haven't seen what second level looks like yet, and I can't speak for the player, but a net gain of 2 HP if you get a 10+ seems somewhat inconsequential compared to what a single monster hits for. So far the biggest impact has been getting a post-Last Breath party member back on their feet. Maybe things will change a bit once we level up.

I'm curious, is the "somebody needs to play the cleric" thing (or equivalent multiclass) one of the D&D tropes you want strongly represented in DW?

Nope. Which is why there are 3 classes beside the cleric that can all heal to some degree or another if they choose to.

Wizard (by being an Elf)
Bard
Paladin

In addition there are 3 classes that specifically let you multiclass to cleric and get the cleric spells, so at second level the Bard, Paladin, and Ranger can all become decent fill-in clerics.

Healing is still a thing and the cleric is still best at it, but there are a number of ways to get healing without the cleric.

Monster damage... of man. I can't say yet because Adam and I want to see it in the text first to be sure, but I think we have that one nailed.

Tease