TLDR, yes we should be removing the broader tag.
For example, with the new bird-identification tag, there were 42 animal-identification questions, 19 of which had to do specifically with birds, so I created the bird-identification tag. It looked something like this,
As you can see, there is now a far more specific tag that has enough questions to justify its existence. Removing the animal-identification while putting on the new tag makes it easier to make sure that I applied the new tag correctly to all of the questions that need it.
There are still going to be questions where the animal-identification is the most specific tag we can use, but it should only be used if there isn't a more specific tag available.
When we create those more specific tags is kind of a subjective thing, but usually once a single topic has more than 5 questions.