If you want your campaign to have a high mortality rate in 5E, it's very easy. Just do two things:
- Ban resurrection magic.
- Eliminate the "dying" condition. Zero hit points equals dead.
That's all you have to do. I guarantee that the result will be a tough, gritty game where people either a) think hard before committing to combat, or b) die a lot.
So the only question is, which should be the default: Lethal and gritty, or heroic and survivable? I strongly favor "heroic and survivable" as the default, and the main reason is the existence of option b) above. People coming into a D&D game for the first time, who discover that their characters die like flies, are apt to respond not by playing ultra-cautiously (which, for a lot of players, is incredibly boring) but by treating their characters as disposable. Why bother connecting with the world, creating a character background and personality, building relationships in-game, when one failed saving throw or lucky monster crit sends all that hard work into the trash? Just roll up Joe McFighter Junior, Son of Joe McFighter Senior, Son of Jack McBarbarian, and be sure you've got Joe McFighter III on hand and ready to go.
The choice to play the game in "hardcore mode" (to swipe a term from Diablo) should be a deliberate decision made by the players and DM. If you're having a tough time selling your players on it, well, go figure, you're telling them you want their characters to die more often! Work it out with them. In general, I believe in giving the DM pretty wide-ranging authority, but this is one area where you really should be forced to get player buy-in. Some people choose to play Diablo in Hardcore mode, and some players will enjoy the challenge of going without a safety net. But if your group doesn't like the idea, it's not the job of the rules to push them into it. It's on you as DM to make your case.
I do hope they include a sidebar saying "For a more challenging game, implement death at zero." But it shouldn't be the standard.