Their most important contribution, long-term, is that the "Disneyfication" of Broadway has cleaned up Times Square and made it "family-friendly". With the burst of construction of hotels and restaurants over the last decade, Times Square is now firmly "cleaned up" and should remain safe at night for many years to come.
I certainly wouldn't want to take my kids to Times Square circa 1980. By cleaning up the area, NY has made Times Square acceptable to families, and it helps make Broadway accessible to everyone.
Of course, everything comes with a mixed blessing.
Although I've seen The Lion King 4 times, and Beauty and the Beast 3 times, this is more a reflection of the fact that I have two Broadway-lovin' kids. These are great starter musicals, and they put on a good show. They've done a wonderful job of restoring two historic theaters. But darn it, they sit down FOREVER...
Broadway's not a theme park, and in order to remain vital there has to be a constant infusion of new major shows. I appreciate everything that Disney's done, but couldn't they rotate the shows a bit more, and create more vibrancy in the line-up? There is a great shot in Broadway: The Golden Age where they scan over the theater listings in the late '50s and it's literally one classic show after another.
Disney perfected the "limited time" marketing technique with their videos (they regularly put classic movies "on moratorium" so that they increase sales in the available period). Do the same on Broadway. Mount more shows, more often, and limit the runs so that each show becomes an event.
Oh yeah, and do The Little Mermaid on Broadway too.