[SHOwnsYou]

There are a lot of trailers made for Broadway. Even tours of Broadway shows have trailers advertising when a show is coming to a city near you.

A lot of plays (not musicals) might not have trailers, I don't follow plays as I do musicals.

But I suspect the reason there are fewer commercials available to a wider audience is actually due to the type of audience they want to attract. Neither theater owners nor performers/actors want the typical movie-goer to be the audience screaming, talking on their cell phone, or generally doing anything against the rules. At a Broadway show excessive phone use or talking can get you kicked out. Trying to take a picture often will get you kicked out.