sorry but I think you are misjudging just how much you learn both grammar and vocabulary from speaking a language natively and possibly misjudging how well education can teach someone a language

languages are these surprisingly complex and irregular things, which are way easier to learn by doing than by trying. often entering school you can already use tenses or grammatical structures that students learning English as a second language will struggle with a few years later in their educational journey, while you can spend that time unknowingly building up an even better subconscious understanding of the language.

It sounds like you are confusing having an ability to speak and understand a language with having a formal education in a language, or just misunderstanding what I was saying. As you point out, people can already speak their native language (more or less) starting from the first day of grammar school. In fact, school isn’t necessary at all for a person to be a native speaker.

The children starting out in school don’t have a clue what a noun or verb is in the language. When someone reaches the point in school where they learn these grammatical concepts, they can do poorly at grasping them or forget about them after they’ve learned them and they are no longer part of the curriculum. They don’t actually need to know these things well (or at all) in order to speak, read, and write. High school students can write an essay in English that shows total mastery of the past progressive verb form without being able to tell you what it is.

On the other hand, when learning a second language (unless one does immersion), a person can’t rely on their native-speaker instinct and therefore will struggle to speak, read, and write if they don’t get the hang of formal grammatical terms to process their language input and compute the output.