Gut instinct says no, this tag would go against all of our tagging principles. Let me try to articulate why.
This tag doesn't reflect a clearly defined concept.
What is popular culture, exactly? For one thing, popular in which culture? Even if we fix a language and time period, different people are going to have different views of where the borderline is between "high-brow" and "popular" literature. Sure, some things like Homer and Shakespeare would be clearly in the former category, but where would the line be drawn? How can we even define the difference? Some centuries-old literature is just a collection of toilet humour (hell, even Shakespeare is full of bawdy jokes); some books published today are written in the style of classical authors from centuries ago. It's not about age, or subject matter, or genre, although all of those things can affect the categorisation. Something that was popular culture in its day might become a classic as time passes. This seems far too subjective and transitory to make a good tag.
Of course there are grey areas with some other tags too: what's the difference between short-stories and novels, or between comics and novels? Some medium-length stories, or heavily illustrated books, might fall in an in-between zone. But at least the concept of a short story or a comic is clear, even if the set of them has fuzzy boundaries.
Also, it's not even a distinction we want to be making.
To be clear, I know that you, OP, are not trying to disdain "popular culture" or portray it as less valuable than "high-brow" literature. But there is a common perception in the culture that "popular" culture is often equated with "trash". Some people even assume the word "literature" to refer only to "high-brow" literature, and think that popular culture would be off-topic for this site. This is an attitude we've tried to discourage since day one of Literature SE: see How will we avoid literature snobbery? and What should we do about snarky comments denigrating specific works? for example. But even so, I know that some users have felt less welcome due to their interest in genres (not even specific stories) that are sometimes seen as trashy pop culture. This is a problem which we want to minimise, and which might be exacerbated by creating tags to divide the site along such lines.
Even though the distinction between "popular culture" and "high-brow" literature does exist in a lot of people's minds (although the line could be drawn in different places by different people, see above), I think codifying it into the tagging structure of this site could be potentially harmful. A big part of the motto of this site has always been that all literature is equally valuable. Tags help to distinguish different types of literature, of course, but making a distinction that people often associate (rightly or wrongly) with quality and/or snobbery may not be a good idea.
Again this does not reflect badly on your intention in proposing a popular-culture tag. You do make some good points, but I think such a tag would create far more problems than it solves.
Yes, different sets of texts/scholarship would be consulted for answering questions about Hamlet or Harry Potter or Onepiece. But that's what individual work and author tags are for: you'd also consult different sources for answering questions about Hamlet or the Canterbury Tales.
The analytical tools used for popular culture and high literature differ most of the time.
This is an interesting point and one that's occasionally caused some friction on this site, e.g. when people familiar with the predominantly sci-fi/fantasy fandom concept of "canonicity" and "Word of God" come up against the more academically literary concept of "death of the author". See e.g. Was authorial intent ever taken seriously in academic literary theory? and What is the history of the universe/canon/word-of-god approach to literature? for some info/discussion around these issues. But it's also possible to analyse popular culture using tools more commonly associated with high literature, and we've already had some Q&A doing just that with interesting results. Again this distinction can be made on a per-question basis: an OP can say what kind of answers they're looking for in each case.
