Native readers will notice those errors, but they won't be characteristic of you. They'll be characteristic of everyone who speaks your language. Nonnative readers aren't likely to notice them at all.
I was imagining a setup like medieval Europe (where international communication is done in a language spoken by none of the parties, Latin) or Achaemenid Persia (where internal government communication is likewise done in a language not spoken by the administrators, Aramaic) or imperial China and its surrounding states (ditto, classical Chinese).
All of this communication is severely crimped by the fact that nobody involved is a native speaker. What happens is that certain fixed patterns from the original language get informally standardized and communication strongly prefers them to whatever alternatives a native speaker of the original language might have used. This lowers the mental burden on everyone.
It also produces extremely stilted and formalized prose, from all parties, which inhibits stylometry. If you only know one way to say something, you'll use it. If everyone else also only knows one way to say that same thing, you'll be anonymous.
(It's possible to study a foreign language past this point. But the overwhelming majority of people aren't going to do that.)
Interestingly, LLMs disagree with you.
Your statement is only accurate in an extremely narrow case, like if you were there to hear the person speaking, before their speech which was transcribed. Obviously, it is not true for almost all of human writing.
And if you were to go commaless, you will quickly get to rather precarious sentences, such as this one:
"Let's eat grandma."
A comma is the natural fix:
"Let's eat, grandma."