Personally, I am a fan of having tags anime-specific and manga-specific, along with related tags for other formats. This solves the biggest problem with the originals, namely overuse.
The main criticism I can see with the tags is that they don't provide much useful differentiation. Most people have a number of series that they are interested in and follow both the manga and anime, and a lot of the other questions will be about things that they haven't even watched. Slicing the other way, namely based on medium rather than series, would seem to be a pretty pointless endeavor.
I would like to argue against that viewpoint. While it is true that the majority of people have favorite series, most people also have favorite media. Currently, two people are following visual-novel and two more on light-novel. These formats are likely to attract a different crowd than most anime and manga, in part because they typically require some knowledge of Japanese.
Furthermore, a lot of people are only interested in canon materials, and want to avoid anything that isn't canon. Those people could ignore anime-specific which would filter out a lot of questions about filler episodes and other uninteresting content.
And finally, these questions can also be about things related to the medium, rather than the content. There aren't many questions like this on the main site at the moment (excluding those tagged as anime-production, which I think is separate), but a good example of a question like this is Why was The Melancholy of Haruhi Suzumiya broadcast out of sequence?. The question is at least partially medium-specific, and likewise my answer was very much medium-dependent. So someone interested in anime in an academic sense would probably have interest in things like this. To be sure, even in the good cases, there's some grey area in which variations and anime-production could also apply to some of these questions, but certainly not all of them.
Of course, all of these are pretty uncommon, and the tags should probably be used sparingly. But at least in principle, they do provide some useful differentiation. I don't think they will be heavily followed, but I also don't see anything bad about allowing them in the modified version.