Well, that does roll back to the OP. Should D&D be explicit in it's player experience goals? Since you are a very big fan of 5e and how it does things, and 5e is fairly explicit in certain areas - such as skills, then I would say that you would agree that D&D should be explicit in its player goals.
The primary difference between how 4e and 5e is presented is that 4e explained WHY these player goals were presented in this or that way. 5e simply presents everything without spending much time on explaining the reasons for why it does this or that. Most of us agree that bounded accuracy, for example, is a good thing. But, AFAIK, that's not actually discussed in the 5e DMG. Bounded accuracy is presented - but, it's never really explained as to why they went this way.
Which, honestly, seems to fit with 5e's presentation all the way along. Very few decision points are ever explained - they're just presented fait acompli.
You can count me among those who think "bounded accuracy" was actually a pretty bad move. Partially because it's mostly not actually having that much to do with
accuracy, and because it really isn't anywhere near as "bounded" as people think, so it ends up being...not really much of anything. It doesn't even rise to the level of a design goal, since 5e violates "bounded" accuracy quite readily if you know where to look, and has done so since at least midway through the original playtest. (Anyone remember the "mid-level Rogue has only slightly less than even chance to tell a lie to
the Prince of Lies himself" thing? Pepperidge Farm remembers.)
It was a very late rulebook for 3E, and probably not a big seller, but I wish 5E could take some inspiration from the Rules Compendium and just talk about this stuff, ideally in the PHB, but certainly in the DMG, even if it's in the context of "we're going to show you how to do horror in D&D, but just so you know, our feelings won't be hurt if you wanted to grab a copy of Dread to use with your Halloween game this year."
Oh, you'll never see that with 5e. We have yet to see 5.5e, so things might change there, but you'd never have seen a product like this for 5e. The obfuscation was never an accident. It was the goal from the beginning. By pretending it doesn't have any specific goals or purposes (even though it surely does, quite specific ones in many cases), they can maintain the
appearance of being a big tent, of inviting folks back in. And then, under the excuse of it being a "toolkit" (despite the many ways it actively resists being used as such), of "kitbashing" or "homebrewing," they can rely on the players themselves to actually do the design (re)work required.
It's quite tidy, actually. Never commit to anything, never give more than wishy-washy "well you can do X, or you can do opposite-of-X, or something in between! It's up to you!", with a steady injection of people literally doing the design work to make stuff happen in the first place, and you can have your cake and eat it to. It can be almost everything to almost everyone, because you avoid drawing attention to how much work they do to
make it be everything they want.
Folks like
@Micah Sweet are generally on board for the general shape and overall kind of game experience 5e offers--but they've realized how little the offered system does to support that experience. That's why they've become rather more jaded about "official" 5e and much more attached to the many 3PP books that rewrite it. (I'd also argue that that's what happened with the folks at Critical Role and, AIUI, several other actual play podcast groups out there; that's why most of them have moved on to other systems or, in some cases, designed their own system.)
I believe that what the OP means to ask is, "Does/should D&D specify what the intended player experience is?"
I agree that the actual thread title makes no sense, as written.
Should they, if they wish to improve the design of the game? Yes. Because being clear about your design intent is essential for getting effective feedback. If you don't know
why something exists, you cannot meaningfully critique whether it's doing its job, to say nothing of how well it does that job.
Should they, if they wish to move units?
Hell no. As soon as you speak frankly with your userbase, they'll fight you tooth and nail about it. Doesn't matter if you're literally just making explicit what has been implicit and intended for decades. Doesn't matter if what you're doing is
literally what their own community conclusions have been for that span of time. As soon as you cross the line, as soon as you actually do stuff openly and above board, you've committed the cardinal sin of
telling them what to do.
Of course, you've
been telling them what to do from the very beginning, since that's what game rules are, literally the instructions for how to play. But as soon as you
show that, oh boy, a vocal minority of the fanbase will be on you like stink on poop, and they are extremely adept at whipping up a frenzy amongst far less invested players.