I was deeply involved in the initial retro-clone phase of the OSR. I was the moderator for the Classic D&D forum at Dragonsfoot and was in contact with pretty much all the main principals. I actually advised the makers of OSRIC to take a different approach other than the retro-clone. (They were smart to ignore me.) Later I helped draft some of the correspondence between the makers of OSRIC and WotC.
Putting myself back in the headspace of an O(A)D&D player circa 2004 and it was a deeply weird time for us in the hobby. Maybe those that have come to D&D since then don't know, or maybe those who were perfectly happy with 3.x at the time didn't realize, but it was actually quite hard to get support for the game then. WotC's pdf program was sporadic, low quality, and was eventually pulled entirely prior to 4e coming out. You couldn't even get consistent access to some of the rule books. The B/X books that are now the basis of much of the nu-OSR weren't ever legally available until 2013. Dragonsfoot and a few other sites put out free adventures, but the copyright propriety of doing so at the time was nebulous at best. There was also a sense that we could get some more and better quality stuff if people were able to sell their products.
There were a ton of products in that era that I called "fishing for grognards." Game products that seemed to be trying to sell to the old school D&D player without actually being the kind of D&D we used to play... Necromancer's "first edition feel," Goodman's Dungeon Crawl Classics, various Gygax products from Mongoose and Troll Lords, Zeitgeist's Blackmoor stuff, Kenzer's Hackmaster. So there was this notion among us that "the professionals" obviously thought there was a market there, but among my circle we were all dissatisfied with the product because it wasn't what we really wanted - i.e. support for the games that we had going right now.
The first time I saw reference to using the OGL to reproduce the 1e rules was on Rob Kuntz's Pied Piper Press forums (long gone, alas), and it was in regard to finding a vehicle for Gary and Rob to publish some of their old Greyhawk stuff. That would have been about 2002, 2003. That discussion went by the wayside when Gary formed a deal with Troll Lords to publish his stuff with Castles & Crusades. But after C&C again disappointed many of us (pretty much all the guys behind OSRIC were play testers for Castles & Crusades) and the Gygax materials from TLG only came out at a snails pace, the impetus for something else came about.
So, the initial push was not to put out some sort of D&D-ish product that met up with certain ideas about how D&D should be played. Nor was it a celebration of general nostalgia for 70s and early 80s rpging. It was quite purposefully an attempt to publish support for specific out of print editions of D&D that were not generally available at the time in a manner in which they wouldn't get sued. No one was trying to exclude other "old school" games from the club. It's just that there wasn't any impetus to make a clone for, say, Tunnels & Trolls or Call of Cthulhu because those games still existed in pretty much the same form as they had always existed and were readily available from their publishers. The whole point was that wasn't the case for old school D&D. Trust me, all the guys involved in that initial retro-clone push loved Runequest, Traveler, Tunnels & Trolls, Call of Cthulhu, WHFRPG, and so on.
Also, I don't think it can be understated how much the "not get sued" part was up in the air prior to OSRIC getting published. It's taken for granted nowadays that if you want to publish an adventure that is roughly compatible with out of print editions of D&D that you can just do it through the OGL. That was not a sure thing at the time. And when OSRIC and the first couple of OSRIC products hit the market, there were some really PISSED people. A lot of folks who were really invested in that whole "fishing for grognards" spectrum of products I described above did not appreciate OSRIC coming along. And WotC did contact the publishers of OSRIC. I don't think I can say much beyond that and point out that 15+ years later, OSRIC is still out and nobody's been sued.
There were a lot of guys who did proof-reading and various other support for OSRIC, but really Matt Finch and Stuart Marshall are OSRIC's daddies. Almost simultaneously, Chris Gonnerman did BFRPG, basically by himself, which is just incredible. Then came Dan Proctor's Labyrinth Lord and Matt's Swords & Wizardry, and by 2008 basically all the pre-2e versions of D&D had a clone ruleset and some support.
To say they succeeded beyond our wildest dreams is an understatement. Guy Fullerton kept a list called
Hoard and Horde which it doesn't look like he's updated in about a year, but gives you an idea of the sheer deluge of support we were finally getting for our games. Literally thousands of products. A lot of it was shovel-ware, but I wouldn't say that was at a greater rate than a lot of the shovel-ware TSR tried to sell us back in the day. But a lot of it was first rate... Gabor Lux's Echoes of Fomalhaut fanzine, the whole Advanced Adventures line from XRP, Anomalous Subsurface Environments, etc., etc., etc. Beyond that, WotC reprinted OD&D and the 1e hardbacks as well a several other hardbacks and adventure compilations, and started taking their stewardship of their older IP seriously with the pdf program with DriveThru, including several print on demand options.
From our perspective, we won. We got what we wanted. Not much else to do other than game. So, it probably shouldn't come as a surprise that the OSR mantle has been taken up by those who are neither satisfied with WotC's version of D&D and who want something different/more than the same old, same old pre-WotC editions. I kind of wish they'd come up with some other term for themselves than "OSR." but it is what it is.