No, unfortunately. That doesn't mean I don't like modern movies or that modern movies aren't good, but modern movies—and here I'm really using modern to mean post-2010, so contemporary movies—have different standards for pacing, characterization, budget, and production that make it harder (or impossible) to capture some of the magic of old movies. Even when modern movies clearly try to emulate that old-movie feeling—I'm thinking of La La Land, The Artist, The Shape of Water, In the Heights—they play the homage too broadly, or they ignore crucial components that make the original films work.
There's kind of too much to go into here without writing a full essay, but essentially, the Old Hollywood system—ugly, failed beast as she was—made some movies simply more accessible to make, due to the ongoing storage of props, sets, master craftsmen, crew, and onscreen talent that could move from one movie to the next without pause. If you needed a dancer, he was already on staff. If you needed a fancy bed, it was already in the warehouse. That kind of longterm storage is invaluable if you want to crank out movies quickly and cheaply because it saves so much time on individual negotiation and sourcing. Modern production companies have to work out individual contracts for every actor on every film; crew members have to negotiate rental contracts and source pieces from scratch; if you need someone with specialist skills, you have to contract them specially at a high rate, which a lot of small companies can't (or won't) budget to do. There's sand in the wheels where there needn't be any. It's wasteful, and costly, but that's the system modern movies are made with.
Which all means that even if the modern movie system wanted to make a classic movie musical just like the old ones, they couldn't, because the talent isn't already there—it hasn't been trained up enough, and there's not that breadth of knowledge you can only get from people who have been allowed to work in the same department in the same place for decades. Movies like La La Land fail, for me, because they present themselves as descendants of Fred Astaire or Busby Berkley movies, while missing the bit where Fred Astaire was a master of his craft. When you watch Fred Astaire dance—or Moira Shearer, or the Nicholas Brothers, or Ann Miller—you are watching a true artist at work, purposely showcased by the studios because they already have them on contract. Modern movies, on the other hand, tend to take people who already have star talent (as actors) and try to convert them into dancers/singers—or they pull dancers/singers off of Broadway, but then they don't have the star power built in. You end up with lackluster musicals where no one truly knows what they're doing, or they do but they're not built up enough by the studios to sell. And that's me discussing just on-screen talent for musicals—there is a huge loss behind the scenes, as well, for all kinds of movies, where roles that would have been filled by union crew who moved continuously from one job to the next have been swapped for freelance labor who live with immense turnover, financial insecurity, and knowledge loss. You could hand me the budget and I could try to make an old movie, but the industry itself has changed so much it's impossible to recapture that charm of steady, niche talent, the amazing possibilities of bonkers set design, and the ability to take a risk on a smaller movie because the other films being produced by the same studio can help balance the budget.
I've talked way, way too much about all of this! Sorry, I just have a lot of thoughts—and the one above is just one of them; the talent loss and storage issues are only facets of a much bigger problem that extends to how we watch movies today, how we market them, what we expect of them, and what's allowed in them. It's a crying shame because the talent is still there, but times change and so does the industry, for better or for worse. (And, just again to clarify, I don't think modern movies are bad—they're just missing a lot of the juice old movies got to play with, even if there's more talent available than ever before.)