A while back I was perusing my Dragon Magazine Archive, and read an interesting article by Gary Gygax in The Dragon #11, Vol. 2 No. 5 (December). The article is titled, "View from the Telescope Wondering Which End is Which."
This article is actually very rich as a spark for a number of discussions. The one I want to visit right now is based on the following quote, "Two years ago we determined to revise the whole of D&D in order to clean up the errors and fill in the holes. The project is a long and complicated one, a task not accomplished overnight. Some players have impatiently demanded immediate release of such material, but we are not about to step into that mess again — D&D originally came out as it did because of demands from those who had tested it and fallen in love with the concept."
The gist of this portion of the article is essentially saying that outside pressure (excited fans) caused the new company TSR to release OD&D before it was ready. The "gaps" in the rules are a result of this. I think this begs the question, even though it is a fairly common assumption, of whether the vagaries of OD&D are a feature, not a flaw....or are they actually a flaw (in the technical sense)?
I think this point is most relevant not in the idea that there should be rules for everything, just that the material present should be explained more completely and better organized. For instance, spell descriptions, monster descriptions, some class info, how the elf works, and a few other things could have been fleshed out.
There are a number of reasons why the revision talked about was handled as "the great split" of Basic D&D and Advanced D&D. Some of these reasons are political and legal, discussed in many other places on the internet, but one reason was to create a "different" game more like OD&D in case TSR was successfully sued by Dave Arneson. There is a nice interview series over at Grognardia with Tim Cask that mentions some of this (Part 1, Part 2, Part 3).
But I just want to hit on a couple of things I've been thinking about. It seems that the idea was that AD&D would take all of the published supplements, merge them, and flesh them out with articles from Dragon, as well as make other adjustments and add extra detail. The real successor to the original three OD&D set is Basic D&D (I'm mainly talking Moldvay/Cook here, since the later sets by Mentzer took on a very different path and the first set by Holmes was less complete than Moldvay/Cook), though while they did substantially clean up the core rules, which I think are much better presented in Moldvay/Cook, a bone of contention many people have is that they altered the generation of characters.
So in the end, all legal and political issues aside, probably the "best" thing they could have done for OD&D, IMO with my armchair designer's hat on, at the time was to essentially take the path of revising OD&D with an eye toward better explanations for the core three books. I think that final result would have looked a lot like Moldvay/Cook D&D (and in fact I think that was what this was for), but probably without thieves and not with a "merged" elf class. It is interesting that later "basic" D&D was seen as the game for kiddies. If that is true, then OD&D would have to be a game for kiddies also since its complexity is no greater. But in reality we are only talking about presentation, and seeing Moldvay/Cook as a kiddie game is only in the context of comparison to AD&D, coupled with the push to sell the new "basic" D&D to kids since the explanations of game play had been vastly clarified.
I recommend going back to read this article by Gygax, it is an interesting window into a certain period of time when D&D was undergoing some interesting changes.