If it is an optional mode, and not what the entire game is centered around (like a rougelike), I don't think re-balance is necessarily needed, or even wanted.
It's a player choice to have death being permanent, to add a bit higher stakes on everything you do.
I think most players will use it when they are already familiar with the game and replaying it, to add an extra challenge.
If the game then suddenly becomes faster, it takes away from the challenge of enabling perma-death, and might even be confusing.
In a survival game, you'd likely want the same survival challenge regardless of if you enable perma-death or not.