Hiya!
Narrative play is a ton of fun, for sure! But, for me at least, there are much better games for it than D&D. Don't get me wrong...D&D can be an almost purely narrative, heroic story of epic proportions, etc. But it's not built...er...let me rephrase that. It
wasn't built for that style of play. With 5th edition, as
@tetrasodium said, the life/death of PC's is MUCH more geared towards life...at least for Players who take advantage of all the goodies to keep their PC's alive and use said goodies without regard for story or "campaign logic" (re: a DM who lets Potions of Healing be purchased at just about any inn, tavern, ale-house, general store, apothecary, etc...for example).
The biggest problem I have with "building more fair encounters" is the very premise of what that naturally entails: The DM deliberately tailoring the Campaign World in order to not hurt the PC's too much. It's like setting up other football teams to play your team...but you always make sure to choose only teams that are less good at playing than your team, except for the big end tournament game...where you put a team that is about on-par...because otherwise your team might loose (or get their...well... you know the saying...

).
What this does, IME, is teach the Players how to "read the DM" and how to "get better at playing-the-DM's-game". It doesn't let the Players 'get better', or have any REAL sense of accomplishment that they
know was all due to their own choices and skill/ability/luck/play. Because they know that the DM is "building encounters for them to overcome in order to push a story idea/goal/plot". Oh, sure, there may be exceptions every now and then...but when the Players know that the only real reason why they have managed to get to the hidden village, venture into the Deadly Valley of Death, discover the Ruined Tower of Mogg, descend into the 4 levels of the Dungeon of Mogg, and finally defeat the Steam-Magicka-Machine-Monster of Mogg and recover the Medallion of Mogg.... is because the DM "built the encounters to be fair" in order for two of the PC's to fulfill some Background Story idea that they had written down, or that the DM had previously planned to reveal once the PC's obtained the Medallion.
In short..."building encounters for the PC's capabilities" (for whatever reason), to me, and IMNSHO, robs the Players of the greatest draw to RPG's: That the Players are the ones making the choices, suffering the consequences, or reaping the rewards. If the game is "built to be fair to the PC's so they don't likely die", well, not my thing I guess. Not for D&D.
BUT... sit me down at a game of Dungeon World, or even something like Powers & Perils or Marvel Super Heroes? I'm ALL for "encounters built for the PC's to have a fair shot" in. Because those games are not D&D. To me, D&D is about going into the dungeon, kicking in the door, killing the monsters and taking their treasure. Everything past that is garnishing.
^_^
Paul L. Ming