The Root Beer Argument is strong.
However, its effect on all the races isn't shown on the shows, and as Edit_XYZ
pointed out, we do have very good reason to suppose that the future relationship between the Federation and the Romulans got worse.
If you turn to the TrekLit novels, in the late 24th century, the Romulans are members of the Typhon Pact
. The bad guys are forming their own sort of federation and have no interest in joining the good guy Federation.