Unless you're listening to 96 kbps Kazaa rips from 2003, better headphones will make music sound better. You might notice that cymbals sound a bit less shimmery if you listen to the same 10-second music sample a dozen times, but the quality drop is so much smaller than the variance introduced by differences in how studios record/mix/master tracks that it's honestly not worth worrying about (except maybe in rare, extreme edge cases).

Note that because audiophilia is fundamentally just dressed-up consumerism, you'll see a lot of this kind of gatekeeping poorly rooted in reality from people trying to seem more refined for knowing how to buy things. It's like how people stopped buying Merlot not because they compared its taste to other wines' firsthand and concluded it was worse, but because a character in a movie they watched once told them that cultured people don't drink it.