The rule doesn't need to change any of that, it is just changing HD healing. It does not change the rest mechanics. Perhaps you are thinking about the variant rest mechanics? Combine this with requiring a healing kit and you have a much more dangerous campaign, IME. Have you tried, because I have.
Injuries, DMG 272 w/ "Lingering Injuries" table
I mentioned save or die in one sentence, that comment was not about that specific type of mechanic, if you missed that, I suggest your read it again. However, I said monster stats are discrete rules modules, just add the more difficult parts of older editions you like. Done.
I don't disagree the game defaults to the easier (meaning less deadly) side. I just find it trivially easy to challenge my players. If you can't that is ok, some DMs can handle deadly 5e and some can't.
However, how many options have you tried? I ask because my group has tried a lot. In fact, we got to a point that was too deadly (using lingering injuries from the DMG was part of that experiment) and had to dial it back. Eventually we found a sweet spot that works for us.