There's a strong overlap between these answers, I'd think.
"Stakes mattering," at least in my experience, almost always involves connectivity to the game world through relationships and goals.
Sometimes, it's just players being attached to the story; goals and preexisting relationships are two good tools for that, but not the only ones.
So I'm wondering what other people's experiences with this are --- what system, group, or other factors combine to make a character interesting, internally realized, playable, and memorable?
For me, I've never had a problem with my characters being interesting to me; I've had issues with getting into character in random gen systems, but never them being uninteresting.
For me, the difficulty of finding the character from the numbers has
always been part of the appeal of AD&D, BECMI D&D, Traveller, Starships & Spacemen, Star Frontiers, and other old school games with random gen. You don't know what you have, and you find out through play.
The one that most encompasses "Find the Character from the Sheet" is Pendragon, when using the random options in 1st to 4th eds. Even the personality is on the sheet, and the rules will guide you to them if you let them. 3 random PCs and see where they take the group...
But I know some of my players don't enjoy that.
I've had some of mine
become uninteresting to me... I figured out who they were, and it was time for them to stop adventuring. They were no longer a mystery, and no longer in need of more...
The hardest part for me is when the players' characters in a game I'm running have become uninteresting to me. That's never good.