Game of Thrones. Interesting and connected characters who get shredded and die…and it’s an interesting and engaging story.
If a player cannot accept there’s risk to a character’s life and limb they shouldn’t be playing a game that’s heavy on combat. Simple as.
Either 1) you want a game that involves risks, or; 2) you don’t.
Either 3) you want an interesting story with vulnerable characters, or; 4) you don’t.
D&D is good at 1, especially older editions. You can force it to do 2, but then why bother with a game as it’s just DM fiat story time at that point. Earlier editions produce vulnerable characters, and emergent stories. If the players find that interesting, great. If not, again, why are you playing the game? If you’re shooting for 4, why?
Funny how LotR gets mentioned in this too. Boromir dies, and... that's it? None of the Fellowship dies. Most of the time, they are barely hurt. So, the notion that you need death to make an interesting story is a bit overblown. And, let's not forget, for all the characters that die in Game of Thrones, most of the original characters from the first book are still alive at the end. It's not like they ever have a TPK in the series. By and large, all the protagonists are still there.
I mean, Harry Potter has a pretty serious body count by the end, but, again, the protagonists are there right the the finish.
Again, this gets back to choice. In older editions, you often killed PC's by accident. It was "Oh, you failed this saving throw, time for a new character". It was almost never part of the narrative. It was just a random die roll. In 5e, you actually have to choose, as the DM, that right now you are going to try to kill that PC. There's very little random death.
That doesn't mean the game is any less risky. It's just less random. And, if the DM isn't willing to take responsibility for killing a PC, then, well, you can't blame the game for being less lethal. Hiding behind the randomness of the mechanics (Oh, I didn't kill your character, the dice gods did) is a cop out.
If you want a game that involves risks, you need to be up front about that with your players. Trying to force your players to agree with your preferred play style by bludgeoning them over the head with mechanics just leads to trivial stories. There's a REASON players don't want to engage with your setting and campaign. If I can randomly die any session, why am I going to bother putting any effort into this character? What's the point? I spend all this time embedding my character in your setting, building up relationships and whatnot, and I die to a randomly generated giant spider?
Let's be honest here. That's cool the first time. The second time, maybe. After the fifth time, well, not too many people are going to put a whole lot of effort in. Same goes with the fifth time you've been jerked around because you decided that having a family was a cool idea.
This is so much of a circular problem. We want players to engage, but, we then punish them for doing so. And rarely does engagement come with any sort of reward. Having a family doesn't help me, it only hinders. Engaging with the setting doesn't make me any less likely to die some pointless random death, so, why bother?
I really don't blame players for not engaging. It's annoying true. And it's something I constantly have to struggle with when I run games. But, I totally get it. We trained the players to be like this and then bitch about it after when they do the things that we, as DM's most reward.