Making it a synonym is fine by me, but shouldn't it point to public-transport instead?
I mean, "metro" and "subway" are clearly synonyms in real life, but on here on Travel.SE they now have different meanings:
Another option would be to have metro as a standalone tag with subway and underground pointing to it. Or maybe rapid-transit as the main term, as Wikipedia has it. Though I'm not sure how much value that would actually add, compared to just using the public-transport tag.
Also, a meta meta question: should
tagging be combined? If there's difference between them, what is it, and which one should I have used in this question? :-)