Hiya!
Will they really? We're on like page 9 and you are the first person on the OSR side to suggest that.
I get what you are saying, but I'm not on the "OSR" side or any particular 'side'. I enjoy all kinds of RPGs, from Rolemaster/HARP, to 5e, to Dungeon World and everything in between.

Anyone who locks themselves into one particular type of game either has very specific tastes, or they are robbing themselves of getting a wider range of RPG 'tastes'.
That said, I *DO* admit that I lean more towards the OSR side of things...I just prefer that overall style of play.
The first half-dozen all suggested that playing with low hit points where one hit will kill you was the source of the fun, and in some way or the other tacitly endorsed character funnels and the ultimate playability (or viability) of any character whether 2 hit points or not.
And I have no problem with that at all. In fact, it is actually quite fun to play a PC with super low HP's. One player had a thief character in BECMI with 1hp. He had a CON of something like 5 (and thieves in BECMI only use d4 for HP!). He modeled the character after Wilfred Brimly (yeah, the rotund old guy from the movie Cocoon and the various oatmeal commercials..."It's the right thing to do...and a tasty way to do it!"

). Even put on a fake beard/mustache and stuffed a big pillow under a flannel shirt. Role played the hell out of it. One of the most fun, memorable characters ever...he was always trying to get, uh, he was trying to convince the lady folk to share some, uh, "extra-special-hugging time" with him (he was old and knew his days were numbered). He made it through one delve into the Caves of Chaos.
So while your answer makes some sense, I don't think it's grounded in reality. Further, if your answer does make sense, then it becomes a table rule of some sort the simplest and least time wasting version of which will be something like "max hit points at first level".
I found what I was referring to in my previous post. From the B/X Basic book, page B6, under "Hit Points and Hit Dice"...
(First level characters may easily be killed in battle. As an option, the DM may allow a player character to roll again if the player has rolled a 1 or 2 for the number of hit points at first level only".
So, basically, anyone who thinks "re-rolling 1st level PC HP's if they are a 1 or 2" is some kind of house rule is mistaken (well, if they are talking about the Moldvey B/X onward; Don't have my earlier blue box and don't care to dig out my little-brown-box books).
Anyway, I'm not really a modern gamer. I'm an "old man" (at least compared to the soccer team I coach or my kids). I've got a grognard membership badge.
This is one example of me being nostalgic:
https://www.enworld.org/forum/showthread.php?580811-Revised-and-rebalanced-dragons-for-1e-AD-amp-D.
But consider both how nostalgic that post is and at the same time how many sacred cows it is willing to BBQ if the drawbacks outweighed the value of the tradition.
You and me both, brother!
^_^
Paul L. Ming