Sure, the costumes do nothing for the plot, but it's the symbolism that matters. Bad example, but you wouldn't do Legally Blonde without any pink, would you? The costumes in RENT don't have anything to do with the plot, no, but they're symbolic to it. The stripper costume and the plaid pants and the Santa outfit and the scarf mean something to the show. People recognize that. It's not "copying" in the sense that you were using the word.
Into the Woods, Beauty and the Beast, RENT, Mamma Mia!, Dr. Jeckyll and Mr. Hyde, Evita (with Julia Murney), Hairspray (with Paul Vogt), Peter and the Starcatchers (with Christian Borle), Lion King, Altar Boyz, Legally Blonde (with Lauren Zackrin).