I think sometimes, yes, particularly when a more specific tag is context dependent on a broader, more general field.
For example, the tag might be used for a question in geometry, or perhaps in a question in group theory (i.e. symmetric groups), or in a discrete math class when the question might concern symmetric relations.
The tag might concern a a question in the field of geometry or analytical geometry, or a question in algebra-precalculus, or in calculus, in reference to trigonometric substitution in integrals.
When tagging a question, whether or can make a big difference in terms of the level of answer to provide.
There are many such sub-topics with tags that are relevant in different, broader fields, and in such cases, including a broader tag can help clarify the context in which a question is being asked.
Another consideration is that many answerers select tags in which they are interested. I, e.g., tend to select more general tags. So a question with only the tag "cyclic groups" may fall under my radar, although I've selected both abstract algebra and group theory as tags of interest. So when the tags chosen are very narrow in scope, there may be many answerers who haven't listed all the 100 or so tags under the umbrella of a general subject as tags of interest.
Basically, I'd advice every asker to include at least one general tag, for the last reason I cite for doing so.