The word "batch" is a general computing term that in the minds of many is not specific to Windows
I agree with the OP that there is a cognitive dissonance in allowing questions about Windows .BAT files to own the tag batch
In the mind of many of us the term batch has a far wider non-OS specific meaning that implies the execution of a (typically large, long running) data processing job that could be initiated manually or via a scheduler.
The batch tag description as it stands describes current usage on the SO site well in that it refers Windows
.BAT files and for some reason SQL scripts. (as opposed to UNIX shell scripts or VMS DCL scripts or whatever scripting languages are used on IBM Mainframes or now that I think of any long running data processing job irrespective the technology used to produce the running process)
Batch is to Windows .BAT script files as Program is to .c C program source files. It's a general term which on SO is applied to a specific concept.
I would vote to change batch to .BAT if that was possible or anything that made it clear that Windows .BAT files were being tagged for discussion.