EDIT: As the OP pointed out in a comment, I have misunderstood the question. It seems that the question is not why some tags have less activity/attention, it is supposed to be "more about the mathematical topics associated with these tags."
I will leave the answer here, perhaps it is still marginally related to the question and it contains at least some useful information.
Certainly there are some areas which do not have enough experts or users able to answer questions from those areas. But your question seems to be more about tags and how they influence visibility of the question.
It is good to add specific tags, but if the question falls also under some larger tag, adding that tag as well might slightly improve number of views.
To stick with your examples, let us have a look at natural-deduction.
I am not an expert on that area, but I'd guess that if a question is about natural-deduction, it will quite often fall under logic tag as well, And perhaps in some cases also formal-proofs and proof-theory might fit.
For any tag you can find out the number of followers of that tag. You can find more details here, but simply said, those are the users who have this tag among favorites or subscribe to email subscription for that tag. Anyway, this number indicates users who are more likely to see questions in that tag and correlates with number of users interested in that tag.
(One disadvantage of the tags formal-proofs and proof-theory is that many people use them incorrectly and add those tag to basically any question which is somehow related to proofs. So your question might get lost among questions using those tags incorrectly.)
Adding a tag which has more followers slightly improves the chances that your questions will be seen. (Of course, you should only add such tag if it is a suitable tag for your question - not simply in an effort to gain more exposure.)