Why would modern Greek be "irrelevant"? Millions of Greeks and Cypriots speak the language, along with minorities in other countries and a very large and well dispersed diaspora. Greece and Cyprus are major holiday destinations for northern Europeans. There are major writers such as Nikos Kazantzakis who have used modern Greek so there are cultural reasons to. Heck, I even like some modern Greek music, and am grateful for it, since it was one of the few things which kept me happy during lockdown.

You're right in saying Classical (inc. Koine) Greek is far more influential, but modern Greek is not "frankly irrelevant".