Hello. I think a save system that reduces or removes the player's score would be fair for a game like this. That way, it works well for both casual players like me, who just want to experience the game, and competitive players.
Another idea I had would be that, instead of having a traditional save system, when you die you lose all of your items, but your level and stats are preserved. This would keep the game challenging while avoiding the need for a conventional save system. The player would still face a meaningful penalty for dying, but they'd continue making progress with each death since their stats would carry over.