Positively, writing everything down shows an openness to possibly relevant material and a communicates a desire to take any information or duties that come up seriously.
Therefore, negatively, not writing things down can display a stance of being closed towards any relevance and a lack of desire to take information or duties that come up with seriousness.
So not taking notes can be a form of dominance.
It might be that you are just wanting to show that you are laid-back or that you have a great memory. And yet even then, this can be a form of dominance:
I'm more laid back than you about these big ideas. You're a slave to organisation. I'm Zen.
And if the person who writes things down is the one who remembers things and reminds you of them later, they are the fussing micromanager, you are the powerful, free-flowing person who forgot all about it, but are happy to oblige once you are reminded.
Writing things down is a humbling inconvenience which shows a willingness to take the other person seriously and engage with them meaningfully and responsibly. Even if you don't need to write things down, it's could be a pretty kind gesture.
