If there is one element of the Old School Renaissance that is the most discordant with me, it is the issue of PC mortality. Or rather, the element I think I would find most difficult to sell to others. The idea is that you're going to burn through a small ream of character sheets as part of the game and that the process will be fun. Or at least have some value. Ignoring the "it's a good idea because Gary said so" element of the argument, the most thoughtful reasons why this is the case are the following.
It encourages intelligent play. If you're going to die from a single arrow to the neck, you're less likely to just start kicking in doors and swings swords around wildly. You have to hire retainers, move carefully, and manage resources. No superheroics and stupid players pay the price. Now this only really works if the GM does a good job of providing sufficient clues for the danger: small details that can reveal the location of traps, or monsters within. Just having an arrow fly out of nowhere and hit someone isn't going to get a person to come back to the table.
It is realistic. Creating the game mechanic that allows some people to take multiple bullet wounds and keep fighting versus the guy who gets shot in the foot, succumbs to shock, and dies has always been the challenge of all "realistic" game mechanics. So individuals who can really only take a couple of serious blows before no longer being able to fight or function is realistic (sort of).
It helps maintain scalability. My browser has red-lined that word so it probably doesn't exist, so let me explain what I mean. If, at 1st level, your PC can take on a small crowd of goblins by himself without too much peril, then in a few levels he will have to be able to take on a small crowd of orcs in order for the game to have some sort of mechanic that reflects both an increased ability on his part and have the GM be able to appropriately challenge the PC for the purposes of drama. After orcs it will have to be ogres, then demons, then a flock of dragons. This is why, if you look in later editions of D&D, you have a paucity of low-hit die monsters but lots of high end ones, because the game needed to have sufficient opponents for challenging high-powered PC's. Compare this to D1-3 in AD&D, where the PC's are still facing troglodytes and hobgoblins.
Those are generally the arguments, offered I feel pretty fairly. There might be others, including the notion that PC's shouldn't have elaborate backstories but rather have the campaign be the story, but I think these are the most compelling. Feel free to suggest others, I'd genuinely like to have the discussion.
Now the counterpoint. Massive amounts of empirical evidence in the form of game mechanics adopted not only by later versions of D&D but also pretty much every other game system that followed suggests that players (to whom games are ultimately marketed) didn't appreciate those arguments. Emotional investment in their characters and perhaps the desire to engage in Hollywood-style heroics meant people didn't like seeing their PC's die. To those who say, "that's emotional immaturity" I humbly suggest that for every six emotionally immature player there's one bad GM who didn't give those clues about the pit trap and instead just sprung it on them. I saw a photo of a gaming group playing Dungeon Crawl Classics where the players were asked to hold up the number of fingers equal to the number of their PC's that had died that gaming session. One person held up both hands. At some point you're getting into Paranoia (the RPG) levels there, and not everyone appreciates that joke.
There's all sorts of activity that subtly reinforces this dynamic, like using miniatures which unless you're using the pre-painted ones requires hours of work to represent your PC. When you've done that, you're going to be greatly disappointed if the PC dies quickly.
Where the rubber hits the road for me is thinking about what game to run after MHR. I really want to do a fantasy game, and would consider strongly an OSR game like Castles& Crusades, but my group has largely grown up on 4th Edition, where PC death is a rarity. So I'm running the same genre, but now death is close at hand at all times. That's represents a real change in the gaming paradigm, if I can use that trite expression. I need to have a conversation with the group before I start planning a campaign using C&C or something similar. If the players really push back, I may end up splitting the difference and go with a 3.X/Pathfinder option instead.