Had She Loves Me opened in time for the 1962-1963 Tonys, it would have gotten more nominations and possibly more wins. In the 1962-1963 Variety poll of New York drama critics, Barbara Cook tied with Vivien Leigh of Tovarich for "Best Performance by a Femme Lead in a Musical," and Jerry Bock won as best composer (easily) and Sheldon Harnick won as best lyricist (even more easily). The Tonys competition in 1963-1964 was pretty intense in musicals, and some choices that may seem odd to us now were made.
Also, She Loves Me won the Grammy for best cast album, which I think you've perhaps mentioned here in the past.
It was in 1963-1964 that the Tonys started moving toward more closely following the actual Broadway seasons. Had the national telecasts not started in 1967, they might have continued on that course.
Also to be noted is that we sometimes look back at the pre-1967 Tonys and give them more importance than they had at the time. It wasn't till the national telecasts that people cared that much about them, something reflected in the relative lack of advertising given to Tony wins (and the virtually nonexistent advertising devoted to publicizing Tony nominations).
Count me as someone who did not like the last She Loves Me revival.