Than you have a misunderstanding in your group, and have to deal with it, as usual. If the group failed communication their respective goals or figure out that the communicated goals clash, they have to find a solution that the game system cannot provide them.
So, IOW, if a system allows for SoD, one set of play groups will have to have a chat about how to deal with it, and if a system does not allow for SoD, then another set of play groups will have to have a chat about how to deal with it? Because, if this is the case, then I don't see how the game having/not having SoD is, in fact, the problem.
What if you play a Call of Cthhulhu game with the intention of running a high mystery horror game, and one player whips out an ex-soldier equipped with an elephant gun and a shotgun and tries to "solve" all problems with firepower?
How long do you try to deal with it "in-game" until you talk with the player that you didn't plan for a high-action/violence game, and discuss how the group deals with that?
My basic philosophy in running a game is that the GM sets up the initial parameters of the world, and runs the NPCs, but doesn't tell the players how their characters may react to those initial parameters. So, I would never discuss it with the group
as a problem per se, but just keep running the world and see what happens.
That is the way, IMHO and IME, the most fun games arise.
(And please note that this is different, IMHO, from bringing a Jedi into the game. I do think that the GM has the right to limit initial player options; this is part of setting the initial parameters of the world. I do not think that the GM should tell the players how their characters react to the world, or how their characters try to solve problems.)
Then you can't use the death-lite approach with that group.
So, basically, if the group understands death-lite you can use it, and if they do not understand death-lite you should not. This is different from SoD how? From where I am sitting, the "problems" are not necessarily caused by SoD (or death-lite) mechanics, but by misuse of those mechanics.
RC
P.S.: Still waiting on those bodak encounter details.