I'd argue that it makes them MORE invested in their characters because they could lose them in a single roll.
This is what we call an argument which on the surface, sounds plausible, but when the idea is drilled down into deeper, doesn't make as much sense as it did on the surface.
A better way to phrase this might be:
"I'd argue that the threat of death makes players MORE invested in their characters because they could lose them."
It's the perceived threat that makes players cautious (be it undead that can level drain as per 3E, or eating a soup that could be poisonous, or just being low level and seeing a Giant and wondering if your PC will survive).
Save or die has nothing to do with this particular set of player behavior.
Save or die just happens to be one type of death in an RPG and typically one that is not perceived until it happens. Hence, save or does seems to make sense in the sentence you quoted, but really doesn't.
Perceived threat is what can make players more invested in their PCs.
Save or Die just happens to be one possible threat, hence, keeping it in the game system to keep players invested in their PCs is not necessary. The DM merely has to threaten the PCs with stronger threats to accomplish that goal.
I do want WotC to bring back threats that are so nasty that the players are cautious around them, but save or die isn't one of them. It's a poor excuse for a threatening game mechanic when the game designers and/or DMs cannot come up with something better.