I like that idea a lot, too.
To avoid it feeling like "Mario has extra lives," I'd rather see it integrated with an alternate start mod, not have you always spawn in the dungeon cell. (That's coming from someone who's never installed an alternate start mod!)
It would be a major undertaking to do it just right... for it to really feel like a new character, you'd want to reset some quests (guilds, etc.) while leaving others completed (major MQ stages, stand-alone side quests). There would need to be new hooks to pick up where you left off; e.g. if the player still has the amulet when he dies, there would need to be some believable way to get it into the new player's hands without relying on (or excessively rewarding) player knowledge of where you died and/or what killed you.