There have been attempts at theater-night life fusions before. Queen of the Night at what is now the Sony Hall comes to mind. Sleep No More continues to operate its show alongside its bar and cabaret spaces. Countless shows performed at venues like 3 Dollar Bill in Brooklyn, the space on 42nd that was most recently the Playboy Club (not sure what it is now), and others. None, save Sleep No More, have been particularly successful.
And none of those were a traditional theater. They were either custom built venues or existing nightlife venues that had other programming. A large theater space, as others have explained, is constrained by zoning and permitting laws. There are also considerable technical and logistical demands here. Here Lies Love is a set in a theatre, it’s not a truly functional night club. It’s intended for a few hundred people to stand sort of dance in for two hours and have an extremely controlled experience.
Moreover, a nightclub wouldn’t support the production financially. The income would go back into the expenses of the nightclub- it would need its own staff, its own technicians, its own technical demands, its own entertainers, and it would all have to be legally distinct from HLL. And the cost of all of this would be enormous.
It’s a patently unworkable and not feasible idea, full stop.
"...everyone finally shut up, and the audience could enjoy the beginning of the Anatevka Pogram in peace."