I feel the more musical genres you are well versed with and know lots of the repertoire the more you understand the larger landscape of the creative arts attached to the piano. I know lots of songs from say Billie Ellish but I NEVER listen to such music outside of lessons lol. You should see the excitement in some students faces when I rattle off works from her or anything else they really like. The more reach you have in the entire repertoire out there the more influence you can have on students and the more vision you have as an educator.
From my personal experience: Whenever I've had friends and a piano in the same room, I would ask them to request their favorite popular songs. If I had heard them before, I would try to play them by memory, on the spot. Otherwise, I would try to transcribe them immediately, and come up with a working arrangement within a few minutes, or something at the very least.
I always find it very exciting. For me, there is the thrill of learning a song super quickly (basically immediately) and playing it as well as possible, and improvising on the spot. Audiences can sense the kind of abandon with which I play, and they love it. Sometimes, there are interesting ideas in the songs which you would not come across in classical music, in the songs. For example, you might on occasion encounter a nicely placed jazzy major 7th chord, or descending left hand chromatic tenths, or whatever else it may be. I find that many of these can eventually work themselves into your subconscious vocabulary (this is obviously much more useful if you compose/improvise than if you solely perform notated works).
I also use the songs to segue into other pieces of interest. You can use snippets of classical music (or anything really), or arrange in different styles.
Anyway, there is this spark in someone's eyes which you can often see when they hear their favorite pieces being played by a musician right in front of them. They can understand it, and appreciate what you are doing, and in a sense, they are able to truly listen, because they have the background for it. You can use that to introduce a lot of different ideas, and they will step in with you unless you go too far out. Once you have their interest, you can often introduce them to different kinds of music. Billie Eilish's songs, for example, are actually decent -- it's just that those with more experienced ears will find them 'boring' and gravitate towards more interesting music. However, if you really listen closely, there is really clever production etc. going on. Of course, we would all love it if our audience can fully appreciate the depth of a Chopin ballade, but it's very rare to find people who can if you sample those who aren't pianists themselves.
If I wanted to introduce someone to classical music, that is what I would do. And I have done this with a few people. Start with their musical tastes, and create a continuous path towards more interesting music. Prime them to
listen and understand it on their own.
This is one of the coolest stories I've read online. Do check it out:
https://www.rd.com/article/the-night-i-met-einstein/I do have a gripe with a lot of classical musicians as well. Quite a lot of them do not have open ears and are conditioned to like the classical sound, while not realizing it. They don't understand or appreciate, say, Keith Jarrett, Art Tatum, or Cziffra, because it doesn't agree with their learned tastes -- whereas a lot of their music is delightfully complex and interesting. I think that there is something to get out of a lot of different styles of music. I remember someone showing me a death metal song, followed by a piano cover of the same, and it was very interesting. Pretty much every classical harmony rule (no perfect fifths etc.) has been broken, and if you can look at the evolution of music from that perspective, it's also quite fascinating.
I really think that the reason why most people who *only* listen to classical do so is because of conditioning, and not because it objectively is better than all of the other music out there. IMO.