I strongly disagree. Grammar is a great tool for an instructor to organize their teaching, but a terrible way for students to think about language. Yeah, to read or speak you need to internalize those rules, but you don't really need to put a particular technical name on them, or think directly about them.

I think the step from "slowly doing grammar while I try to understand" to "I'm so good at grammar that I just understand" doesn't work that way.

I was taught English from 6 to 18 in a very traditional, strict, grammar-driven way and learned nothing. All spaniards go through the same type of lessons and very few can understand anything at all after years.

At 18 I stopped any classes or studying but I got satellite TV, English computing magazines and shortly afterwards the Internet and then just learned all the English I needed to get by without much conscious effort.

A few years ago I got interested in Danish and in about 4 months I could read regular novels at a decent pace just from Duolingo, newspapers and subtitled TV series. I probably could do the same with any language just with enough motivation.