I think the "complete" musician is one who always strives for perfection, but realizes that it's a lifelong process. Ray Brown was a major influence in my life. I saw him a week or so before he died in his mid 70's. He was giving a free lesson to a promising player (something he did in every town he visited before his performance). He learned from others. I recall a lengthy conversation he had with Victor Wooten. He was trying to explore Victor's sound and how he could apply playing techniques to upright.
He was as close to a "complete" musician as I've ever known.
Russ