So: Old school D&D is a terrible system for playing the game most people want to play when they pick up something called "D&D," not having any prior experience with old school D&D. The texts don't do a great job of communicating their purpose, and honestly, the other things that people want to do are fun and it's reasonable that they want them.
One of the big things that people want when they pick up something called "D&D" is a game where they get to craft exactly the guy that they want to play. Old school systems by and large do not deliver this, especially on a mechanical axis: Your initial character generation is random, and your advancement is usually relatively fixed and relatively random.
The thing is, most of the folks I've met like that got into the game before I got them-- middle or high school, or occasionally college. These are people who saw "fantasy adventure game" and opened it up to find that there was also a bunch of math and were super happy about it. (I'm in that camp myself-- I've had few happier days than the one where I discovered the interlocking logic of the 3e EL and XP tables.) But there's a big, big pool of people I've gotten into the game who got scared away by all that math and all those decisions, even though they desperately wanted that fantasy adventure.
But those people already get enough air time in the OSR. One of my favorite things about old school D&D is that it's made it much easier for me to run games for a mix of highly invested and brand new players than any other edition I've encountered (except maybe also 5th-- still gathering data). While really serious D&D strategists will get annoyed by the shenanigans the newer, less death-hardened players get up to, it's much easier for brand new players to contribute to the gamier side of the game than with the newer, more character-build focused versions. You don't have to read the book and absorb the rules system to play a really powerful character in old school D&D: You just have to be quick on your feet, and the right mix of careful and reckless.
Random chargen helps make generating a new character fast (important when death rates or high, or you're playing with different people every week so you need to be able to get the new guy into the game fast) and can create interesting tactical and expressive challenges for experienced players: "Well I would never choose to play this guy but now that I've got him what do I do with him?"
Fixed advancement and random advancement also make leveling easier and faster, which is important when your character is more a token that lets you interact with the game-world than an end to be developed in itself. It also really helps players who like developing their character's personality but either don't care about or actively overwhelmed by mechanical differentiation.
In general they all can make getting into D&D a lot less intimidating for new people. Generally my experience with getting brand new people into 3x/Pathfinder has been "Oh my god I have to read that entire book? Oh okay, just these bits... uh... which feats do I want... wow, it's going to take us a really long time to make all these characters, this is kind of boring."
My experience with getting brand new people into old school D&D has been more "Oh my god I have to read that entire book? Oh, okay, just these bits... rolls stats my intelligence is really high so I guess I'll be a wizard... oh wait no, I want to be a bard, my charisma is really low but that will be hilarious."
Or even "okay, so what are all these numbers on this index card? oh, okay, you'll tell me when I need them, cool. oh, sweet, I have a grappling hook, I wonder what I can do with that."
Not that Pathfinder is a bad system for newbies-- I've played with new-ish people who expected mechanical character differentiation from video games and were disappointed/frustrated by old school games because they didn't provide that. One of the things I like about 5e is that it potentially bridges the gap between those folks and the systems I like.
The old school character generation and advancement are also fantastic for the players who want a strategic resource management game that's mostly about their lateral thinking cleverness. For those folks, choices about what widgets to give their character would be choices they weren't making about things that they care about.