And still, for all the value in first-rate theater that “Good People” stands for, this example of copycat programming raises some questions about the creative health of the regional theater movement. For a decentralized performing art form that needs to maintain strong community bonds, is lock-step play selection an encouraging trend? “Good People,” after all, is not the only play of recent Broadway vintage suddenly showing up on the marquees of major nonprofit theaters all at once. Several other plays that ran on Broadway in the past few years, including “Clybourne Park,” “Other Desert Cities,” “The Mountaintop” and “Time Stands Still” are also being produced by 10 or more companies around the United States in the 2012-13 season.

In fact, according to the Theatre Communications Group, the trade organization for America’s nonprofit theaters, nine of the 11 most-produced plays this season opened on Broadway over the past four years. Only “The Whipping Man” (from off-Broadway) and “A Raisin in the Sun” (from 1959) don’t have newly minted Broadway pedigrees. In Washington, performances began on Wednesday at Studio Theatre of one of those 11, Stephen Adly Guirgis’s “The Motherf---er With the Hat,” which ran two years ago on Broadway. In March, Arena is host to Katori Hall’s “The Mountaintop,” a commercial success during a 117-performance stand on Broadway that ended in January 2012. And in April, Jon Robin Baitz’s “Other Desert Cities” settles in at Arena, following a seven-month Broadway run that ended last June.

There’s no shame in offering accomplished works to audiences in cities that otherwise would not see them. (And what would the most-produced list look like, after all, if these works weren’t on it?) In the past, when straight drama was a more front-and-center cultural force in American life, commercial producers might have sent these plays on national tours, with some or all of their original Broadway casts. With the rare exception of a piece such as “War Horse,” plays are deemed too financially risky for tours these days. Still, the duplication of offerings is not what you’d call a point of pride. Some artistic directors at theaters whose identities are forged by unique choices of plays express a bit of embarrassment at what appears to be play selections made in a mind cloud.

“I have to remember I’m programming for a D.C. audience and not for the artistic directors of America,” said David Muse, artistic director of Studio Theatre, one of nine in the nation producing “Motherf---er” this season. “On the other hand, I hold onto this idea of regional theaters as art houses, and wanting to have distinct artistic identities. Like with many things, it’s just a question of balance.”

It is, of course, far easier to schedule a play that has performed well elsewhere, than to subject a company perpetually to the rigors of otherwise untested work. Some theaters say there is an absolute obligation to get these works in front of their audiences. “I think it’s the responsibility of theater companies to do a play like ‘Good People,’ the same way a play like ‘Red’ has to be done in different parts of the country,” said Molly Smith, artistic director of Arena Stage, where the Tony Award-winning “Red” played a year ago to enthusiastic reviews and crowds. “Good People” is a wise and funny play that asks pertinent questions about social responsibility, about what specifically those who rise from humble origins might give back to those they left behind.