I like this, there's almost too much to respond to
I'm just a newbie to piano, 2 years total and half of that was just dickin' around. Most everything in classical is still pretty new to me (non-piano music is also very inspiring), but I can tell some people are sick to death of hearing certain things. As much fun as I get out of playing Haydn sonatas, it bores my teacher, I won't be subjecting him to any more alberti bass

I have never heard any of this material, but I got interested in Satie and just buy collections of his music and play my way through the books. In a month or two, it will not be Satie but someone else.
My music teacher really liked my playing Tuesday, particularly what she referred to as my interpretative abilities with the material.
We went on and had a talk. She asked me why I persist in finding out-of-the-way material and feel motivated to play it.
I told her, "it's an alternative to playing Fur Elise for the 500th time, or playing the Moonlight Sonata or the Pathetique Adagio movement, or Turkish March or all the rest of this much-played student repertoire."
I'd say this is human nature; being attracted to new things, novelty seeking, curiousity. I tend to be the same way in buying collections and being obsessed with some new composer, except it takes me much longer than a few months. Then, this seems to be what you're saying all along, the 'new' composer for me is what is old and tired to you.
Although I've managed to avoid Fur Elise so far (as leahcim said; "everyone does so don't say Dali") I've decided to learn it anyhow, and learn it damn well... Not so much for myself as for all the non-musicians who would like to hear it, again.
It's occurring to me that most people aren't so interested in hearing what I like to hear, no matter how well it's played. There just isn't much of an audience for the less well known music out there. I figure I can appease their 'Fur Elise-tooth' and maybe they'd be more receptive to whatever else I'd like to show them...
Some unknown stuff is just more attention grabbing to the layaudience. Unfamiliar Beethoven sonata movement gets to more ears than any Haydn sonata I've ever busted out. A lot of Bach is especially hard to listen to for non-musicians, I usually like to prepare a listener before Bach (this is the motive, this is an inversion...). Sometimes a person is just more receptive than other times. Randomly.
A more musically aware audience might be more pleased to hear the 'Tempest' or 'Apassionata'. Since we're picking of Beethoven, an audience of pianists might be sick of those, maybe op.90 or op.2no.2 would be more interesting? Like I can play any of those

I believe the audience is important, you must be able to connect with your audience. I can't stand learning all kinds of pieces and forgetting them before having a chance to share it with somebody.
Leahcim mentioned composing and improvisation (in a different context

) and I think those are be
great ways of connecting with the layaudience. I've always thought the chorus of Britney Spears 'oops I did it again' would make a great fugue subject. One day I hope to pull it off, it would be hilarious and people would love it... Or a theme & variations on some popular melody. I heard a radio interview where a pianists (can't remember who) was playing a Mozart PC when he'd rather have been at the premier of the second Star Wars, at the cadenza he improvised over the Star Wars theme. Those who caught the reference loved it. I don't think classical musicians pay enough attention to improvisation and composition.
Whatever strangeness my curiousity brings me to, I'll still need Fur Elise, The Entertainer, etc. for engaging the audience.