Really? What about Srinivasa Ramanujan, a self-taught mathematician whose solutions to problems were generally considered completely novel and unconnected to other's results. Eventually he worked with Hardy, but sadly died early.

Or Alexander Grothendieck, who when given at university a choice of 14 open problems to pick one to work on one over a period of several years, solved several within months. Again he had a mixed experience of early training, and worked independently at first. Of course, he later collaborated with many others.

Newton literally said "If I have seen further it is by standing on the shoulders of Giants" because he acknowledged that his work built on that of others. Indeed, if he had communicated his results earlier, maybe he would have worked with Leibniz on the calculus.

While people do like to focus on a singular visionary - rather than a history of invention or scholarship - that does not mean that there were not extraordinary individuals in history. Yes, they also had to be in the right place and the right time. They also had to have the time (usually, enough money) and the connections.