Surely what we're talking about here isn't so much about academia relating to music or piano playing as relating to life in general. Most people not working in an academic setting don't actually need many skills or much external information beyond basic maths and literacy and some specific job-related knowledge. You can live a full, useful, creative life having never really engaged your brain at all about anything that doesn't directly affect you.
The question is, what are you interested in and how do you want to pursue it? If your goal, in piano playing or anything else, is simply to do it to the best of your ability and to play it how it feels right to you, you need never seek knowledge beyond what you need - for piano, the ability to count to about 16, recognise symbols and then the manual skills of hitting the right keys in the right patterns will do fine. It works for a lot of people and some would argue that it makes you the best, most creative pianist you can be, even if you aren't sticking to the letter of the composer's intention.
I believe in setting a rather broader agenda, and besides reading include things like attending concerts or the theatre regularly to hear other musicians, and travelling to visit the places that inspired the things I'm interested in. I'm very lucky, via work, to be present at a couple of concerts or shows every week, and in the past I have played with, and run, a very good amateur orchestra. Hence I have a background in music and performance, and learned to appreciate other instruments and styles that I would never have considered otherwise.
Among other things, my academic background runs to a degree in physics, and one of the things I love about playing a piano, or any other instrument, is understanding the principles that create the sound, and that form the harmonies in the music.
Anybody with manual skills and a little basic knowledge can read music and play a piano. Or do brain surgery, by stretching the argument rather. What you need to develop either one beyond your own personal skill and interpretation is a frame of reference, and that means exploring the culture and literature of your chosen subject until you don't just perform but understand why and how you perform. There must always be direction and goals... if your only one in playing the piano is to play a particular piece, what are you going to do once you can? Will you just stop there and be satisfied, or will you look around you and discover the next particular piece, and the next...
Background knowledge in itself won't make you a better pianist, but it can help and inspire you to be one, and that's the true purpose of any learning.