If the teeth are together in a grin, the mouth is closed, and the lips don't play a factor in this. See grin. The :D expression can be achieved with a grin, and there are many examples of this which show a :D expression but are closed_mouth, such as post #3820667 and post #4353068.
But :D expressions CAN involve a grin. Take another look at the examples.
Which is why I think the examples shouldn't be tagged as :d. Even if the mouth is formed like a D, I think that :d should always be an open mouth. And even then, you could argue, that the grin depicted in the examples is an open Mouth by how far the lips are apart. (Which I wouldn't say, given the Wiki, but you could argue for it.)
To clarify my argument a bit more: I don't see the reason to tag :d together with grin. Someone searching for grin would only want to see clenched teeth together as a smile. They don't care about the form of the mouth, and even then only for evil grin, I guess. On the other side, someone searching for :D would want to see images of a person really smiling at the camera or w/e, only seeing upper teeth or lower teeth or none of the both, but the mouth had to be opened. You argued forum #180529 for normal users having to add or exclude tags to search for stuff, but your suggestion here only adds more trouble for them. Someone wanting to see :d with open mouth would have to search :d open_mouth or :d -grin etc. It would be way more easier to just garden the tag and exclude all the :d + grin cases IMO, as the form of the mouth isn't important when searching for grin.
:D is just the shape of a d-shaped mouth. And that is mostly a smile + open mouth.
But apparently you need parted teeth as well otherwise it's not an "open mouth" (I don't agree with that at all but seems like most of this topics disagrees here).
But anyways, it's just a shape and shouldn't imply anything more than what it describes: A smile.
Another case of an old "convenient" tag being taken too literally in the modern day. :D was created way back when autocomplete didn't exist as a shorthand so you could represent the specific expression without multiple tags and didn't need to type something like "widely_parted_lips_smile_with_teeth_apart." Given the original usage, :D is a grin without the teeth together (and grin is a parted lips smile with the teeth together) and thus they'd never mix, but given the non-descriptive nature of the tag and wikiphobia it's since evolved.
Another case of an old "convenient" tag being taken too literally in the modern day. :D was created way back when autocomplete didn't exist as a shorthand so you could represent the specific expression without multiple tags and didn't need to type something like "widely_parted_lips_smile_with_teeth_apart." Given the original usage, :D is a grin without the teeth together (and grin is a parted lips smile with the teeth together) and thus they'd never mix, but given the non-descriptive nature of the tag and wikiphobia it's since evolved.
This is honestly how I always looked at that tag and used the tag.
Like some of the others, in my opinion :D and grin are mutually exclusive for a single view of a character. I don't think I've ever tagged things like the examples as :D.
There are legitimate uses of grin :d solo (post #852404, for instance) but goodness that tag search is filled with junk (post #159687 is surprisingly not atypical)