GRRM was a D&D fan back in the day, so the death penalty in his books was potentially adding flavour to the loss of Con and a level.
My players don't really like it either - they always try to find a way to make it so their character doesn't have to do anything for four days so they can just get rid of the penalty. [Which is not to say that I always let them, but then they grumble about having to remember what the penalty is and when to apply it and so on.]
What if, instead, being brought back from the dead worked more like it does in Game of Thrones? That is, you would still have the scars showing how you died, and you'd "lose a bit of yourself" every time. Reading through the various related spells, it seems like raise dead already does this to a certain extent, since resurrection specifically states that it restores any missing body parts (which implies that raise dead does not). The harder thing to model would be the losing a bit of yourself.
You let your players avoid the death penalty by napping for a few days, not pushing any deadlines or saying a certain amount of adventuring has to be done.
Do you think you'll be able to enforce a longer lasting and potentially more impactful penalty, like an insanity?
Okay, scars. You could get the players to narrate how they kill key monsters, or how they are knocked down. If they die from the wound, it just gets worse, but how it's described and where it is, is determined by the players.
Flaws are cool, and would be an interesting way of adding some lasting impact to death. However, this means the players have to choose to play up the flaw, and might get rewarded for doing so with inspiration. They're unlikley to let their flaw take over during a stress moment.
Are you familiar with FATE compels? Where the storyteller offers a Fate Point if a player acts out a personality trait. This could easily work with flaws: the DM offering inspiration with the reminder of the flaw, and the player either takes the inspiration and acts based on the flaw, or rejects inspiration and has to describe overcoming the flaw.