Timing is everything.
I think that if Next to Normal, Grey Gardens, or Passing Strange opened this season, it would be the frontrunner for the Tony for Best Musical. None of this season's new musicals seems to be hitting that sweet spot of critical praise and audience response. While these 3 musicals didn't hit that sweet spot perfectly, they probably come closer than any of this season's options.
If it were still open, I think Finian's Rainbow would be the favorite for Best Revival of a Musical.
It doesn't sound like Spider-man was really ready; if it had been rushed through, it would have gotten some tech recognition but I think it would have been panned.
"What was the name of that cheese that I like?"
"you can't run away forever...but there's nothing wrong with getting a good head start"
"well I hope and I pray, that maybe someday, you'll walk in the room with my heart"