Tags, as I see them, have three major roles to play, under ideal settings:
They hint the reader what sort of topic the question will be, before opening it. Thus, using correct tags will help increasing the exposure of the question to its target audience.
They help partition the database into more manageable parts, and eases up searching, browsing, and using the site.
They help the answerer calibrate the level of the answer. If someone asks about continuity of a function using real-analysis, the answer will be different than the same question tagged under metric-spaces or general-topology.
Having too many tags on the site causes too much fragmentation, and may lead to questions having less exposure than ideally. So having specialized tags for specialized topics should be introduced when they help compensate for an actual problem.
The reason is that it is likely that some new users will put a specialized tag as their only tag. If you have a tag for the prime numbers theorem, and only three people follow it, a question which only have this tag, would have received a lot more attention if it had been tagged under number-theory (for example).
It is true that when a tag becomes sufficiently big, it can be useful to add specialized tags to help users navigate that mass of questions. But this still runs the risk of underexposure if not used correctly. And if something can be misused, it will be.
So if a tag does not help searching for data, does not help predict the content of the question, and does not help the answerers to anticipate the level of answer... it should definitely not be introduced.