I am somewhat a bit torn apart about this proposal.
That is mainly because none of the tag usage guidelines is particularly good and can't be easily understood by new users.
I think stereochemistry is already quite broad, at least broad enough to warrant sub-tags. The usage guideline only reads
Refers to the spatial arrangement of atoms in a chemical entity.
This has pretty much the same meaning as the usage for molecular-structure
This tag should be applied to questions that deal with the particular arrangement of atoms in a molecule, the so called molecular structure or geometry.
I think there is a lot more to stereochemistry than only talking about stereoisomers, as it is a subdiscipline of chemistry.
For example, there could be a question about the creation of an asymmetric element, manipulation/ modification/ annihilation/ retention of a sterocentre, properties of stereoisomers, stereo-discrimmination, reaction-mechanisms, etc. pp.. I have not checked the 300+ questions so I am not sure what the most used purpose is. As such it is more like an umbrella tag like organic-chemistry.1 Or does the tag really just mean stereoisomer?
The tagname chirality refers to an optical property. The tag-usage does not reflect that:
For question relating to isomers which cause plane polarized light to be rotated in opposite directions.
So the tag according to its usage actually refers to enantiomers. As such it clearly is a subgroup of stereoisomer, and at least a specific point of study in stereochemistry.
In general, however, I don't even see that chirality clearly corresponds to a subgroup of stereochemistry. Therefore I think tagging a question with only chirality is perfectly valid; for example, if a question asks only about the optical properties of enantiomers, I would hesitate to tag it with stereochemistry.
If we follow through with the argument, then we need to merge geometrical-isomerism into stereochemistry, which should be merged into isomers. And why not merge everything into molecular-structure? And where does symmetry fit in; and what about conformers? I don't think that having a tag that is used almost 100 times is overly-specific tagging madness. I think it is a specific enough tag to have merit on its own - it doesn't even hurt the question if it's the only tag that is applied; sure, there is overlap, but is that really a bad thing?
I'd also like you to consider that we created a whole catalogue of tags for functional groups to have a better classification, so why not have the same for subgroups of isomerism?
What we really need is a better usage guidance for these tags.
1 Which is a horrible tag to be searching by. As such, it doesn't really have a good purpose.