”Stop playing” also has meant returning to play absent the possibly deep history of the character in the ongoing story. The old character might take away too much information or might have been carrying too much of the story.
I don't think that it's appropriate to focus on the idea of "stop playing" as the reason character death (or equivalent loss of a PC) is the reason why it's the only really significant consequence in an RPG, to the extent that if you give players the choice you'll find that the only things "worse than death" are things that also take away the character.
I think the issue is that players have a relationship to their player characters equivalent to a person has to a highly valued material possession of some sort which they value not primarily for its cost, but because of the journey they have taken with it and the sentimental value they attach to it. Think of the value attached to an old car which you've done the work on yourself or to a painting that you yourself painted or a vase you made on a potter's wheel and you kept because it was the first one you really felt proud of or that house that was a fixer upper that you made into a home or your original wedding ring - whatever you can think of that you value above just being a thing.
Not every player does that, but in my experience the vast majority do so such that losing that PC hurts as much as losing something "real". Sure, you can replace it without too much trouble in most campaigns, but you will as you say lose the story the PC is carrying and the history the PC had that you'd built. It won't be the same, at least not at first.
And the reason that no other consequence is significant is because no matter how invested the player is in other elements of the story, they've never invested nearly as much time into those things as they have into the PC. So the vast majority of players in a long running campaign will always prioritize the PC over any other story element - winning, NPCs, fictional positioning, etc. Generally speaking, players will treat any crash they can walk away from as a good landing. They may want vengeance on an NPC afterwards. They may want to restore their PC's name and honor afterwards. They may want to do a lot of things to recover from the consequence, but the point is that that is fun and they get to do it with their PC. None of that is really failure. That's emotionally success with minor consequences that propel the story forward. That's more history to the PC that increases the PCs value.
Things that permanently cripple a PC can be equivalent to death, and indeed can be perceived as worth that death because they attack the mental image of the PC and in some systems are harder to recover from than death - a more permanent loss. But that has I think already been well covered, both by myself and Lanefan's creative list of ways to fail.