Definitely unnecessary for them to be a part of every educated person’s library. This is a pretty absurd viewpoint. The reality is that there are loads of educated people who contribute vast amounts to the world without even the most passing familiarity with “modern math”.
I also don’t agree with the sentiment of the rest of the post, sorry. If someone is casually or recreationally interested in math, building a comprehensive view of modern math just… isn’t important. If you’re interested in spending more time with math, just do it—don’t let the perfect be the enemy of the good. There’s no right approach other than the one that makes you happy.