If you look at B/X, most of the rules are to do with exploration, then combat, with a smattering of social rules (reaction rolls, hiring mercenaries, charm person -- though the latter could be viewed as combat). Though it's true - some OSR games leave all that stuff to fiat, and only have carefully delineated rules for combat, usually justified with that argument that combat is where the game most needs to step in and provide rules, not rulings.
It *is* pretty counterintuitive though. "Combat is usually a bad idea" is usually an emergent property of the ruleset and is often a lesson that needs to be learned. PbtA games do a much better job of using basic moves to set expectations. Now I don't think that makes the PbtA approach *better*, a OSR ruleset can also just say "hey, treasure=XP in this game, so killing monsters is an unnecessary risk. Think about avoiding them or stealing from them instead". But because many OSR games assume an experienced audience, that advice often gets left out.
I agree that death is often an uninteresting consequence. Some OSR players definitely enjoy the revolving door of characters and black-comedic deaths. I think for others, it's more about the *threat* of their character's death to make consequences feel real. And because OSR generally doesn't go for illusionist DMing, that threat needs to be backed up.
Some people instead go for "your character becomes increasingly scarred", but I think my next game will instead go for forced retirement except in cases where survival is absurd. Your character is still around, but they're an NPC now.