"Sondheim is a composer...Disney is merely a producer. It's not as if Michael Eisner has composed the music and lyrics to all of the shows running. Each show has a different composer and book writer...making them COMPLETELY different from one another.
So your example fails to prove a point."
Disney may be the producer, but it is the same Disney creative team that creates the animated movie behind the musical. Most of these movies and the resulting shows have exact same characters (handsome prince, the beautiful princess, the bad guy, the funny sidekicks) and musical numbers (inspirational ballad, rousing energetic number, bad guy's evil plot song, romantic ballad). Disney movies may have different individuals creating the shows, but they all have the same "Disney" feel to them, which does tend to overshadow the talents of the individual creators.
The average person walking down the street may not know that Alan Menken and Howard Ashman wrote the music to Beauty and the Beast, but they can definitely idenitify it as a Disney show. Using the example from my previous post, I don't know who produced Sweeney Todd or Gypsy, but I can definitely identify them as Sondheim.
It's not necessarily about the individual creators, it's about the overall feel of the shows. Having 5 Disney shows running simultaneously will definitely influence the way Broadway is perceived, in the same way so many musical theater fans complain about the Andrew Lloyd Webber/Cameron Mackintosh monopolies in the 1980s.
Like a firework unexploded
Wanting life but never
knowing how