Has never worked in the past?
I'll give you one game that used this business model in the past. It had a simple core, playable in any number of ways. It had three classes, all weapons did d6 damage, some methodologies to build your dungeon and your wilderness settings. It was entirely contained in three booklets of around 36-42 pages each.
You're conveniently forgetting the part where your hypothetical 5E could simultaneously be several different games often with completely incompatible gameplay. OD&D didn't do that. And it's specifically that kind of multi-system / dual-statting support (which is what you'd effectively need) that has failed time and time again in the RPG industry.
As I've said before: I get that you really, really, really, really want 5E to be OD&D with all the stuff you don't like pushed off into an unsupported supplement where you can ignore it. But it's fairly clear that it's not going to be.
However, a Fighter who has gone on to become a Thief and thence a Bard (the first prestige class; and it was a bad idea then, too) is not just a Fighter any more, making the comparison pointless.
But at that point you're just saying that you prefer one form of customization vs. a different form of customization. Which is, of course, perfectly OK. But it's a very different claim.
The OD&D rules Cyclopedia had things like Paladin and Druid (and several others) being classes that were entered after getting to name level.
As others have pointed out
OD&D != Rules Cyclopedia. I cited 1985 because I thought it was the year that both the BECMI Companion added druids/paladins and the year that UA added NWPs. But a quick review indicates that the BECMI stuff was actually 1984. So call it 1984-1985.
4E is d20 at its core. All you got to do is find a way to emulate 4E by using the OGL/SRD itself while not infringing on WotC's copyright (which means some terms would not be used and replaced and so on). Which is totally possible, and has been done as you know with the other editions of the game (retroclones).
It's a very different kettle of fish: 3E streamlined the core of the game (while keeping most of the math the same), but left most of the ancillary stuff (monster descriptions; spell descriptions; etc.) intact. The ancillary stuff is the stuff most likely to be protected by copyright, so the OGL gave the retro-clones the ability to re-apply the original core mechanics (the stuff that explicitly can't be copyrighted) and run with it.
4th Edition, OTOH, kept the core mechanics of 3E but changed everything else. The difficulty and legality of making a retro-clone of 4E that's acutally compatible with 4E (as opposed to just having some similar gameplay with radically different classes, powers, monsters, etc.) is much, much higher.