The concepts of "man" and "woman" are already doing a lot of work in language, society, law, etc. Redefining those terms would cause/is causing a lot of upheaval.

Think of the concepts of "citizen", "resident", "immigrant", "ex-pat", "DREAMer", etc - all terms related to where someone lives and what set of laws applies to them. Regardless of how the person feels, the label isn't just for their own sake. Someone can be a citizen and an immigrant if they are naturalized, saying someone is a resident implies (but not definitely) that they are not a citizen, ex-pats are assumed to be temporarily in the place where they reside.

Labelling trans women as women is a lossy translation that ignores a lot of societal edge cases.