I've been to all 4 Broadway Center Stage events at the Kennedy Center. They're in costume, complete script, mostly off-book and minimal set design. It's not a full production, with sets flying in and out, and elaborately choreographed numbers, but with the casts they're putting together, I've never felt I've missed out.
Kennedy Center did stage their own productions off and on for a few years, and Ragtime and Follies both transferred to Broadway, but unfortunately neither were financially successful.
The National Theatre is just a venue, not a theatre company. They don't create anything themselves, the shows there are just leasing the space.
Like a firework unexploded
Wanting life but never
knowing how