Paladins do have an OH SHIT button. They have several, in fact. This is, historically-speaking, a very OH SHIT-oriented class. They're just not group/raidwide and they require some outside-box thinking and cooperation/coordination with the affected parties. So they don't seem as useful in the current game.
Lay Hands, BoP, Divine Shield, and HoSac can all stop, with quick reactions and 1 GCD, a death from happening — just like that. It's "Nope. You're not dying." The end. No arguments. It's somewhat distinct to Pally healing.
The problem with LoH is that tank healing isn't really a 'job' anymore with Active Mit so aggressively in place, and it's not something you stack CDs for. And for non-tanks that suddenly drop, you can usually provide enough healing to get the same end result with much simpler/shorter CDs for example a Shaman's Mastery+UL+AS+GHW or even just a timely crit from IoL DL.
The problem with BoP & HoSac is they're creative use of game mechanics and require split-second coordination with multiple other players to use them effectively as an OH SHIT button in the good sense, instead of "OH SHIT we just lost 4 extra people, thank you idiot healer".
The problem with Divine Shield is of course it only affects you, and there's been a creeping infection of abilities which just go "LOL NICE TRY PALADIN" right through it as the xpacs wear on.