I think this thread could've been ended much sooner by someone just saying YES, its best to learn everything you can, not just piano, but whatever you can learn will make you better, no matter what field your in.
I mean does this really even need to be answered?
Thats like asking if I need to learn how to pour cement to work in construction. No, you could avoid learning, and just pick up trash at the sites instead. Or, you could come with enough money and buy the company and hire someone else who knows the business to run it and you'd never need to know anything about pouring cement, but if you knew how to yourself, you'd save yourself alot of money paying someone else to manage the site.
Same thing with Piano, or mixing, or guitar, or any aspect of making music. Few have mastered every aspect of making music themselves. So there will always be the need for help in certain areas. Maybe you can write, but can't play. Or maybe you can write and play, but cant mix. The whole point is the more you learn to do yourself, the more money you'll make, and the less ppl you need to depend on to make your music.
If you don't know how to play piano, and can afford to play someone else to play, thats great, but you still have to worj around that persons schedule, as well as pay for his services.
Learn to do it yourself and you can make music whenever/wherever you want yourself for free.
That applies to all instruments and all of the jobs in the business. You won't be able to master all of them, but pick and choose to learn the one's of most importance to your craft, and the more you learn, the better. As well as the more chance you have of finding work. The more skills you have, the more jobs there will be available to you, thus the better odds of breaking into the business.