I see where you're coming from, but personally I really appreciated the depiction of an introverted main character. Also both of his sons were consultants on the film and apparently supplied part of the dialogue and tone for the scene where he talks to them before leaving for Apollo 11 [1], so that part of his relationship to his family, at least, seems pretty accurate to me.
One thing I remain curious about is how serving in the Korean War shaped the psychology of that first crop of astronauts. And I would LOVE to watch a movie with the budget and talent of First Man, but about Yuri Gagarin or Valentina Tereshkova.
[1] https://www.nytimes.com/2018/.../first-man-ryan-gosling-clai...