It's not contradictory because my hope for this is realistic; I don't want the rules to have lacking areas, but I recognize that there's no way for any game system to cover everything - that's simply impossible.
I see a difference between my original statement of "I don't want them to have lacking areas" and "I want nothing excluded." It's certainly possible for rules to act as guidelines without having to necessarily expound upon everything (I didn't play 4E, but from what I hear the "page 42" rule was a lot like this).
I'm not sure what you mean by "disqualify it as a valid area of concern." If there's something I want the game to do, it should ideally provide a framework for how to do it, or they'll cover a given idea to the extent that any gaps are so small that they can be covered by flavor text alone (e.g. there's no "solder" class specifically, but the fighter is so close that you can just say your fighter is a soldier - if there's no class that lets you possess other people's bodies, that's harder to fill with a reskinned existing class).
Now, the latter example there is a fairly extreme one, but I've had players ask to play a sentient couch before, so these things come up. I'm not saying these aren't understandable gaps, but gaps do happen (which is another reason why I want 5E to be under the OGL - so someone can cover these odd corner-cases).
Okay, so you really mean "I don't want them to leave
significant gaps." How would you go about determining what gaps are generally significant? Personally, if the game lacked a magic class that specialized in possessing people, I wouldn't consider that a gap. I'm hopeful that the majority of DnD DMs and players would consider the sentient couch thing an extreme corner case.

But there's always that one guy... However, given that
that guy exists when somebody suggests:
If there's something I want the game to do, it should ideally provide a framework for how to do it, or they'll cover a given idea to the extent that any gaps are so small that they can be covered by flavor text alone
to use as a standard for evaluating mechanics for inclusion. Well, that's highly variable depending on the "I" in question. How does a game designer or editor decide what should or shouldn't be there? Personally, I've come to think that there isn't any objective way of determining it. Since its all subjective, I prefer making that subjectivity as easy to support as possible.
Depends on who you ask. A 1E-style wizards is pretty basic to me, but I play Pathfinder, so take that with a grain of salt.
Sure, but compared to a 1e fighter...
I don't think this is necessarily true. While there is a connection between rules and playstyle, I think that an expansive playstyle doesn't necessarily "lock down" the system from smaller changes or additions. Now, if you want "significant deviation" then I'll grant you that it is harder to do so under an expansive system...but if I wanted significant deviation, I don't think I'd be playing that game to begin with.
Of course, that was another benefit to the OGL, in that it let other companies deal with those problems and resolve them when they offered a significant deviation of the game.
I'd agree with the OGL sentiment, but I think it makes even more sense to make the core simple. Back in the halcyon days of 2e, campaign worlds varied wildly, and even more wildly as they added more "options" books. Individual DMs (to start with) had to make several decisions about how various spells worked. Seeing unique classes and spells was very common. A simpler core may require more houseruling, but it makes it much easier at the same time. (Also, simpler games are generally much harder to "break".)
I understand your sentiment about playing another system, but this is a social activity. I cannot go off and play FATE by myself. I belong to a gamers meetup group for my area. Its currently (last time I checked, anyway) dominated by Pathfinder games. Hopeful players of other games rarely manage to arrange a group, even though I live in a pretty densely populated area and people seem willing to drive for games. 4e players were even having a time of it for awhile.
D&D is "the granddaddy" of rpgs. At least for fantasy, I'd like it to be a flexible, central point for everybody to converge on. It needs to cover a wide variety of playstyles. In that aspect, anyway, it needs to be more like 2e than later versions of the game.
I didn't feel that it was there, at least not very much, in 3.5.
It was, but it was not a design goal like 4e, just a side effect of the rules being written the way they were. To be fair, it did play to the dominant type of DnD games out there at the time 3e came out. That's explored in plenty of other threads, though.
That said, we seem to be talking about slightly different things...you're talking about adding house rules because you want to (e.g. you feel you can do X better), whereas I'm talking about adding house rules because I (perceive a) need to (e.g. because X is broken, or simply absent altogether).
See, from my perspective, you too are talking about adding house rules because you want to. Adding a separate class of magic users that work differently isn't a gap in the rules, its you making your campaign unique. How many different ways are there to make Magic Users? I dunno, but I don't want to carry the rulebook that covers all of them. (I can think of at least 4 from the 3e era that collectively would make a book larger than the PHB.)
I'm talking about having my campaign/gameworld to run the way my group wants it to (at least within the realm of DnDish fantasy). However, I
also want your group to run the way it wants. If one of our preferences interferes with the other, then I prefer that to be the exception (a module, a houserule, or whatever). The more expansive and comprehensive the "core" of a game is, the less flexible it is that way. I've played a lot of Indie/alternative games and that just seems to be the case. (Although
extreme simplicity or minimalism has its own problems, and "wouldn't be D&D" to most people.) Its far easier to start with a very simple core and add modules or houserules to suit than it is to start with a system of everything and ask the simple or alternative folks to pare it down to the game they want. It also works with their preferences to do it this way. The designers hit this one spot on.
The big difference (I think) is that I don't view a houseruling as a bad thing or indicative of a broken or incomplete system. As you said, no system can (or should) cover everything. The GM will have to make decisions, judgement calls, houserules (even as specific as "No, Invisibility and Fly cannot affect the same whale he targetted with Animal Friendship. You may not have an invisible sentient 30-ton flying battering ram... ...again." Don't laugh, that was my first 3e game). The guy at the head of the table making those kinds of decisions is part of the game, not a failsafe external to the game.