Right from the beginning, these recent arrivals didn’t like what they saw on Broadway. New York’s most widely circulated Spanish-language newspaper at the time, La Prensa, called for a picket at the premiere, and the Puerto Rican journalist and labor organizer Jesús Colón lamented that the show was “superficial and sentimental” and “always out of context with the real history, culture, and traditions of my people.” In subsequent decades, this tradition of protest and critique has only grown richer and more collectively exasperated.

Mr. Bernstein’s music and Jerome Robbins’s choreography are often cited as the musical’s redeeming features by its liberal defenders; a critical Los Angeles Times review of the 2009 Broadway revival nonetheless praised the “extraordinary variety and operatic fullness” of the score and the “ecstasy” of the dance numbers. But I’ve always been baffled by how the musical’s creators squandered the opportunity to engage the genius of Afro-Caribbean polyrhythms. The gym scene “mambo” is not, rhythmically, a mambo, and the famous rooftop number “America” has the Sharks dancing a Spanish-from-Spain paso doble mishmashed with whitewashed showbiz jazz.

When performers like Ms. Moreno succeed in conveying distinctively Nuyorican ways of moving, they seem to strain to do so under inhospitable conditions. In theory, “West Side Story” should have something to say about the experience of assimilation. But in practice, the musical demands assimilation from its Puerto Rican performers, then capitalizes on the glorious virtuosity of their capacity to resist it.

Directors of more recent productions have made an effort to adapt “West Side Story” into something culturally relevant and a bit more politically correct. The 1980 revival was the first to cast a Puerto Rican performer as Maria, and the 2009 revival enlisted Lin-Manuel Miranda to render some of the dialogue bilingually. In the latest Broadway staging, Mr. van Hove dutifully follows their lead: The Sharks are played by Latinx performers, and there are snatches of urban Spanish patter between songs. The bodega looks like a real bodega.

And notably, the choreographer Anne Teresa De Keersmaeker leaves behind the soaring lines of Jerome Robbins’s original numbers in favor of loose, feral syncopations developed in collaboration with the dancers themselves. Of course, there’s only so much Latin rhythm they can bring to the musical while maintaining a working relationship with Leonard Bernstein’s score — perhaps an object lesson in the limits of reform, whether aesthetic or political.

Where Mr. van Hove diverges from previous stagings is in doubling down on the plot’s brutality. I still can’t shake the chill I felt watching the Jets attempt to gang-rape Anita in the show’s third act. It’s magnified on a giant screen onstage, captured by one of the Jets on his cellphone camera. The omnipresence of screens in this production should remind us how easy it has always been to reproduce, revive and restage scenes of spectacular violence. Yet I’m not sure how deeply Mr. van Hove understands the implications of his own choices here.

According to Scott Rudin, one of the show’s producers, Mr. van Hove “doesn’t direct revivals like they’re revivals, because to him, they’re not.” Mr. van Hove may have “no iconic relationship” to “West Side Story,” so he may not feel the oppressive repetitions of the history of violence against brown women bearing down on his body. But for many of us, it’s the umpteenth time we’ve seen Anita assaulted for dramatic effect, each time under the guise of greater authenticity.