Actually, I grew up here as did many of my family and friends. We all tend to dress nicer for a Broadway show, we grew up doing so and continue. I also do the same seeing a performance at Lincoln Center.
This. It's the tourists who are mostly in the casual wear (most people I know going to the theatre [I mean people I know who live here]) either get dressed to go out for the evening or they're going from work, so they're nicely dressed either way.
I've wondered why the tourists tend toward the beyond casual before, the 'they don't dress for community theatre' thing, I suppose but...why wouldn't they dress nicely to go to the theatre even if it's a smaller venue? Nevermind that now, they know where they're going so why wouldn't you bring something nice to go out for the evening to nice places?

As above, at the ballet and opera, which tend to attract mostly locals (dunno why that either. heh), the crowd is MUCH better dressed. Kids are pretty much all properly dressed for a show (party-level dresses, mary janes, suits or button-downs at the least), adults in nice stuff, etc.