I understand his point - the best theatre in New York City doesn't always take place from 41st to 54th Streets, with a quick detour to Lincoln Center. Over the past few years, I've seen terrific off-Broadway productions and some Broadway shows I could have missed.

People who tune in Sunday to watch the Tonys (8 p.m. CBS), including some of the tourists who buy 65 percent of the tickets to shows, are watching because they want to see "Broadway." No disrespect to the rest of New York theatre but I think that's pretty indisputable.
The Tonys and Broadway are inextricably linked in the public's mind. It's "Broadway's Biggest Night." And Broadway, for better or worse, has name recognition.
The Broadway League and the American Theatre Wing have a stake in protecting the Tony Awards brand. Once the Tonys become a mix of Broadway and off-Broadway, you've diluted the brand in the eyes of the viewing and ticket-buying public.
Besides, even if off-Broadway shows were eligible, it still wouldn't make Gerard's last statement true:
"Off-Broadway has been playing the supporting role for way too long. It’s time for the Tony Awards to invite everyone into the tent and give real meaning to the phrase 'outstanding achievement in the theater.' ''
If you really want the awards to reflect outstanding achievement, then you would have to include all of the great work being done by theatre companies across the United States, not just give out one regional Tony per year.
All you would accomplish by including off-Broadway is to turn the Tony Awards into "outstanding achievement in New York City theatre." And I'm sorry but that doesn't sing quite like "Broadway."