Well, what do consider William Klein to be? (No, I don't compare myself to him.) Some icons of fine art photography did some commercial work, Saul Leiter for one, but most are known for their personal photography, or better yet, art. I guess it is possible that Klein just stepped out on to a sidewalk and without much thought made photographs that hang in museums, but it's doubtful.
Klein. He left the American forces and as part of the GI Bill, got himself into Paris and became an art student under Fernand Léger. He was primarily an artist in the painter/designer sense of the term, and then moved over to photography where he did good work in fashion (possibly starting the craze for long lenses after some striking shots in Rome) after discovering how he could use photography to illustrate movement of tones and turn them into something quite other than what they had first appeared to be. This was as the serendipitous result of seeing some large, painted screens being moved whilst they were suspended from above. His interest in film led to other work too.
But this is all beside the point: he is an artist in various mediums, and I have no more idea about the ins and outs of his work than anyone here. His street work for
New York was done whilst he was living courtesy a grant/contract from Vogue which, eventually, was stopped because of the perceived anti-Americanism of that body of work and it was only published in America because the French published it first. Robert Frank redux? Now, are you willing to call that street work personal or commissioned? It was done on Vogue time but not to their pleasure. He went to Rome, Fellini offered him a job as an assistant, but the movie was delayed or scrubbed, so Klein spent the time there making another book: Rome. Again, what category would that fit? Nobody commissioned it.
The truth, insofar as I can glean it to be, is that Klein was ever his own man, and whatever he did, paid or otherwise, was to his own tastes. I consider that to prove that the two positions are certainly not in permanent conflict, as I found for myself in a far more modest way. I produced calendars for various companies, but they were created mainly to give me the photography I wanted to do, and earn a buck at the same time. Waiting for the 'phone to ring wasn't going to get that done - I had to arrange all those balls. If I'd relied on the 'phone, I'd have ended up shooting babies and bloody weddings!
Don't forget: photography as art, in the gallery sense, has been a relatively new concept that was quite well established in America by the 70s or so, but struggled elsewhere.