The touring argument is valid when it is an tight race. When A Gentleman's Guide to Love and Murder's won over Beautiful, we have to remember that the race wasn't so much Gentleman's Guide vs Beautiful as it was Gentleman's Guide vs After Midnight. The only reason Beautiful was even in consideration was because both Gentleman's Guide and After Midnight, were limping toward Tony Night. Beautiful on the other hand was the season's surprise sleeper hit with the powerhouse performance of Jesse Meuller, akin to Sutton Foster in Millie, and Idena Menzel in Wicked, both of whom she competed against for Best Actress.
When it comes to Fun Home vs An American in Paris, there really was no race. The problem was the Fun Home being an Off-Broadway transfer from the prior season was ineligible for all Drama Desk, Drama League, and Outer Critics Circle Awards, allowing An American in Paris' producers to play the momentum card. The entire Broadway community as behind Fun Home, and if that happens there are not enough road producers to outweigh that. When there is no race, people try to create one to keep things interesting.
There are 3 examples in recent memory where the Touring producers can be seen playing the deciding factor for Best Musical, Wicked vs Avenue Q, Billy Elliot vs Next to Normal, and Once vs Newsies. In the former it is documented that many touring producers were upset when Avenue Q canceled its national tour in favor of a sit down production in Las Vegas, as they said that was the only reason they voted for it, believing Wicked was an easy sell, and if Avenue Q won Best musical they would have 2 easy sells to their subscribers.
Regarding the second, Next to Normal was the opposite scenario, where after being burned by the Avenue Q, producers first didn't trust that Next to Normal would actually tour. Second that such a small show with no eye catching visual and a cast of 6 that was currently playing to an intimate house with less than 800 seats, couldn't possibly work in touring houses with 3000+ seats. The ironic thing to that reasoning is was that just as the Avenue Q was angered tour producers by not actually touring, Billy Elliot's tour tour was a financial mess with the sit down production in Chicago, and having to change producing companies within the first year of the actual tour. All this while Next to Normal actually did pretty well on tour.
Then for the final, which is somewhat the place we are still in, many road producers believed Newsies was an easy sell on tour regardless of whether it won a Tony as its a Disney show. On the other hand, many road producers believed Once needed the Tony to make it a must see on the road. In other words, similar to the Avenue Q vs Wicked, why present have only one must see in your season when you can have 2.
This year seems poised to be a very tight race between the artistic innovation masterpiece that is The Great Comet, the critical darling and surprise juggernaut box office hit that is Dear Evan Hansen, and the feel good musical of the year Come From Away. First of all 2 of the 3 are ineligible for all of the pre-Tony awards since they are off Broadway transfers. I wouldn't be surprised though if The Great Comet's producers try and get it eligible in all of the technical awards since this is technically a completely different production that was "inspired" by the off Broadway production considering its been so radically redesigned going from a sit specific production to a proscenium stage, as well as a "revival" as it had been approximately 2.5-3 years since it closed off Broadway. Add to that we still don't know how Groundhog Day will be received so either Come From Away Or Groundhog Day will likely sweep the pre-Tony awards, allowing them to campaign as the "Most Award Winning Show of the Season." Due to all of these unknowns and the fact that is such a close race, I honestly do believe road producers will be a deciding factor.