I see this type of like used to justify whatever it is the speaker enjoys being forced on everyone else. Something like "everyone should learn philosophy because it trains the mind" usually means "I like philosophy and wish it was taught more at schools".
I think it depends on what you think education is : if you believe that education is going to an elite university then I think it is elitist. If you think education is being exposed to a wide range of ideas and perspectives - a range beyond which you would have found by yourself - then I don't think it is. A kind Aunt with three bookshelves and an open mind can give you an education that you couldn't buy. Would that make you part of the elite? It would be difficult - it could take years - but it's not elitist.
Every discipline (academic, artistic, practical, even athletic) deal with certain types of problems and have develop their own heuristics for dealing with those problems. And because most discipline involve not a single skill but a set of skills, some disciplines will have skill overlap.
If you play music, run your own business, study (or practice) engineering, or become involved in an academic discipline you develop a set of skills you can carry to other domains. Don't really see how the dispute here