What would be a history of science?
It is easy to make a list of scientists and weave them into a kind of story, although the tendency of biographers to make errors of science is problem. But a history of science and not just scientists, would weave the biographies into a specific kind of narrative, based on the idea that science progresses, if fitfully, by absorbing new dimensions of truth, brought into view by individuals, not by flopping from one idea to another.
Such a history would show how a field develops from idea to idea, each new step correcting some things, supplementing others, but always necessarily incorporating the factual observations of the preceding generation, and showing why previously accepted principles looked right but included an error.
The fashion of saying that truth changes from generation to generation is specifically anti-cultural and it is present even in the natural sciences.
How would such a narrative look?
In [some ancient time] a scientist [name] discovered or just thought out [something], which was of crucial importance [briefly explained], and for a number of years, people either worked out the implications or argued with him. However, his ideas [were incomplete or had an error built in], perhaps for philosophical reasons [such as...] or perhaps because of bad or misunderstood observations by [himself or other people], and so, after a while, the field got stuck.
Then [at a specific date] along came [someone] who saw what was needed to get going again. His insight caused a great stir, and there might have been opposition of various kinds [such as]; in fact, his thoughts may have been buried for [decades or hundreds of years], but in due time, truth prevailed and things went forward.
But of course this was still not the whole story, and in fact, science got stuck again, needing a better understanding of [something] to go forward.
Then [at a specific date] along came [someone] who saw what was needed to get going again. ... etc.
Who can write it?
Such a history of science could only be written by someone who knew both science and history; furthermore, he would have to understand some philosophical issues, and he would have to be free of political pressures to make the narrative look a certain way or to leave out certain people, or to exaggerate the importance of others. Each biography would be included simply on the basis of how that person developed, or hindered the development of, the field.