I don't think the majority of Tony Voters, when voting for Best Musical, have at the forefront of their minds "I'm voting for this show to save Broadway!" or "I'm voting for this show because it needs the support!"
I think the primary reason why a voter casts their ballot for a choice is strictly financial (ie what do they have to gain, financially, from the vote). And if they are not financially impacted from the vote, then the secondary reason is "which show has friends that I want to help benefit."
Then lastly, if neither of those two things are a factor, then one may vote for some other reason, such as "voting your heart" for the "best," or "a vote for this show sends a message."
"The Spectacle has, indeed, an emotional attraction of its own, but, of all the parts, it is the least artistic, and connected least with the art of poetry. For the power of Tragedy, we may be sure, is felt even apart from representation and actors. Besides, the production of spectacular effects depends more on the art of the stage machinist than on that of the poet."
--Aristotle