Cats is an old, polarizing property and an odd choice to make into a movie. I would attribute any issues with/repercussions from the movie mainly to that. I would not read too much into the long-term effect on the genre. Rent and The Producers both flopped in the same year, but numerous movie musicals came out since then, which cost a lot more money to make than those two films.
I grew up at a time when the live-action film musical was DEAD and no one thought it would come back. Since Chicago reversed that trend, we got Phantom, Rent, The Producers, Dreamgirls, Hairspray, Mamma Mia, Across the Universe, Sweeney Todd, Enchanted, Nine, Rock of Ages, Les Miserables, Into the Woods, Annie, The Greatest Showman, La La Land, Beauty and the Beast, Mama Mia Here We Go Again, Mary Poppins Returns, and Cats. I am probably forgetting a few. Some of these tanked, some did quite well. Some were loathed by critics, and some won Oscars. Such is the business. Then there were all the live television musicals—let’s not forget those. No one could predict this resurgence. I would not place bets on when, how, or if it will end. And sometimes genres do need a break because of audience fatigue, and then they come back years later.