Same here. I've heard somewhere, in a video about language acquisition, that we have a pattern recognition algorithm in our brains, so all we need is to see examples, and the algorithm does the rest (builds a model by itself).
Research from the 60s up to the current day has pretty conclusively shown that language acquisition only occurs through comprehensible input (this is known as the "Input Hypothesis" popularised by Stephen Krashen) and that deliberate learning of grammar and vocabulary has very little to no impact on your language skills. Basically, our brains all learn language in the same manner no matter what language and no matter what age. Children don't learn their native language through reading books on grammar, they acquire it through listening and reading stories which they can comprehend. Adults are exactly the same.
(The theories of the existence of a physical module in the brain or innate universal grammar are not widely accepted science today, but it is inarguable that the above second-order effects have been observed regardless of the mechanism of action.)
(1) is somewhat true while (2) is utter garbage. In fact, the point of (2) is to reach (1). In his book, Nation (2001) explains very well, with data from numerous studies, that cramming vocabulary is in fact an extremely optimized productive use of time and effort. And given how Nation details the dimension of vocabulary learners, he is above suspicion in respect to being biased towards rote learning.
However, consciously learning grammar definitely does not have significant enough returns to be worth the effort (it can help somewhat in certain cases, but comprehensible input has a much larger effect).
Personal experience however tells me that explicit teaching is a good way to know what’s going on, which is very valuable for highly grammatical languages. Again, in a perspective of "bootstrapping". I think what institutional language teaching is missing is that the needs of students, and thus the effectiveness of various methods, change with their proficiency. Like the fact bilingual dictionaries are better for beginners or intermediate learners while monolingual ones are more suited for advanced ones. Sadly, too often teachers (as well as students) are trapped in dogmatic approach where something is either good or bad on the whole spectrum...