Revisiting this years later now. Is there a reason to keep these concepts separate?
While gi and dogi are training uniforms, the inverse is not true. (Not all uniforms are gi or dogi.) We would either have to expand uniforms to cover every type of uniform, or allow individual kinds of uniforms to crop up.
Personally, I think having a simple training-uniform for all kinds of uniform has potential to both hurt and help. I suspect we get the most gains with this tag if we advise people to also tag their questions with whatever martial art they are interested in. So judo and training-uniform would be about Judogi and brazillian-jiu-jitsu would ask for about the uniform they wear in that martial art. If that usage guide is in place, I think it will work well. If that isn't there, I think the unified tag will waste people's time.