This is closer to a comment than to an answer - however, it would be too long to be posted as a comment.
One important thing which might help to judge whether or not the tag can be useful is the intended scope of the tag. Currently the tag-excerpt and tag-wiki simply describe what Hamel basis is. This makes it definitely more specific tag than the previously existing basis tag that was created and removed several times in the past. For past discussions of this tag see, for example, Can we delete the [basis] tag? and Tag management 2015. For a short period, there was also a tag called basis-dimension.
When I see the tag hamel-basis I can see two ways in which tags might be used. EDIT: As explained in a comment, the OP created tag with the second meaning in mind. I.e., basis in vector spaces (not exclusively infinite-dimensional spaces). I have included this clarification in this post to make it visible a bit better than it would be in a comment.
Typically, the distinction between Hamel basis and other types of basis is only needed if we are working in infinite-dimensional spaces. That is also the reason why very often a student does not encounter the name Hamel basis in an introductory linear algebra course - although they are in fact working with Hamel basis. So one possible usage is that this tag is intended for basis in infinite-dimensional vector spaces. I would imagine as typical posts in such tag the ones originally tagged by the OP or questions such as: Can a Hamel basis of $\mathbb R$ over $\mathbb Q$ be measurable? How do I show that infinite-dimensional Banach space has (Hamel) dimension at least $\mathfrak c$?
The other possibility is that the word Hamel in the name of tag is used mainly to distinguish this tag from other types of bases, but still includes the finite-dimensional case. So, for example, tag-names such as basis-vector-space or basis-linear-algebra could serve basically the same purpose - to make a distinction from base for a topological space, Schauder basis, orthonormal basis, etc. In such case I would imagine here many questions of the type where basis tag was used while it existed. To list a few typical examples: How to find a basis of intersection of two given subspaces of $\mathbb R^4$? How to find a basis of a given subspace with contains the following vectors? How to find basis of kernel and image of this linear transformation?
It is also possible that the tag is intended for both types of questions described above. (Well, if we have a separate tag for basis of a vector space, it would probably not be useful to exclude infinite-dimensional spaces.)
I can see some merit to both usages. Still, before discussing this tag further, it would probably good to know which of these (related but still a bit different meaning) was intended by the tag creator.
The tag of the same name was created a removed in the past. (See also Asaf Karagila's comment in chat.) Looking at the questions where the tag was used, it seems that the intention of the user adding the tag was the meaning 1 in the above list. As far as I remember, there has not been discussion on meta explicitly about this tag. (Although the past discussions about basis might also touched on Hamel basis.)