Honestly I think it really depends on how you look at it.
I do agree that the world of classical music has become somewhat stale and out of touch with the rest of the culture (at very least, American pop culture). This partly has to do with, a, the tendency of the wealthy, snobbish upper classes of the early 20th century to "patronize" the arts. Example: Andrew Carnegie. And it isn't limited to the 20th century--Beethoven, Mozart and Haydn dedicated almost all their music to the gentry who supported them financially, regardless of what they actually thought of those people.
The other issue nowadays is that the classical music world is so addicted to tradition and familiarity with the greats. Now, I love Beethoven and Chopin and Rachmaninoff as much as the next pianist, but and each one loved and respected the ones before them. But at the same time, each one had their own vision of what music could become, and could see beyond the world around them.
Now to answer your question: What do I think the purpose of being a classical pianist is? To put it another way, why do I love music so much that I want to play it for other people in hopes that even only few people from an audience of hundreds or thousands may be uplifted and encouraged? I don't know, really. But I'm a very empathetic person, and I communicate much better through music or poetry than through plainspeak words (and I love all writing in general). I know there are people out there who will understand me, and who be blessed by it.
Now does this necessarily mean being a concert pianist, with the suit and tie and all that? Not by a long shot. There are a lot of musicians out there who play for the same reasons--not necessarily classical music, but I respect their choice mode of communication. If they put thought, practice, and heart into their work, I respect it, even if it's not Rachmaninoff or take-your-pick classical composer.
Does this make sense?