I think that whatever value you add, it won't necessarily change player behaviour; some people just run ahead at full speed until they fall down (dead or dying). Sure, you might find some players become more cautious, and avoid anything that puts them in danger of dying, but even then a lot of people will only learn the hard way, and some never learn...
After all once upon a time in D&D a Wizard started with 1d4 hp, and died at 0; a Fighter started with 1d10 hp, maybe a Con bonus, and died at 0 hp. Did those players behave with great conservatism, only engaging in lethal combat as a last resort, or did they charge in swords and spells flying? In my recollection, when I was a kid playing Basic and AD&D, my players pretty much charged in like they were indestructible, and I encouraged that by fudging a lot of stuff. Later, we added more hp, and it did nothing to fundamentally change the way my players approached the game.
I think if you take away the "dying" mechanic, to "actually you are dead", you still need some way of showing the players "hey, you are going to be dead soon". Adding X hit points to the base, doesn't mean they will pay any more attention and die less, unless the game actually enforces some kind of explicit "check point" that forces the player to make a decision on whether to carry on or seek help. The 5e dying mechanic, isn't perfect, but it at least forces the player to recognise that their PC is nearly dead (it also forces them to do nothing, but hey, it's not perfect).
So I think rather than just add X hp to the base, you also need to add some kind of check-point, like Bloodied was in 4e, that says to everyone "hey, from here you're getting close to dead dead". At which point you need to decide what it is, as obviously it can't be falling down unconcious (or you've just re-created the existing 5e rules). But I think you need something, that has an in-game impact, otherwise you've just given the players a lager pool of hp, but exactly how they interpret those and what they do about it, will vary wildly. For example, someone who has 20 hp, vs someone who has 5 hp - will they approach the game any differently?