As someone finally noted along the thread, how about asking what genres we are talking about before making recommendations?
If you want to sing opera (or even Broadway), without proper training you will get nowhere, and likely wreck your vocal cords in the process.
If you want to play classical piano, not only is the training intense, but it is lifelong. No home-trainees need apply.
If you want to play jazz and you don't have your chord theory down, along with real improvisational skills, you don't get to join a top-end band.
If you want to sing in a gospel choir, simply having big pipes isn't enough, you have to learn to sing 'within' the choir, the dynamics of it.
As for the snarky statement that "those who can't, teach" the late Professor Gunther Schuller is a worthy counter-argument. He was involved with just about every genre you can think of, playing, composing, arranging...and teaching. He was far from the only one, but he was a giant in his own way in what he contributed.
Kenny Aronoff, one of the hardest-hitting rock drummers out there, studied classical and Jazz in college. He has also been an Associate Professor of Percussion at Indiana University.
C.