The Dutch are extremely proficient in English because they teach their children in it from 8 years old. And have been doing it since at least the 80s.
So while what you're saying is technically true, a lot of shows were only subtitled instead of being dubbed, it is also factually false, that is not the main reason for the proficiency.
No we haven't. I'm Dutch, I was in primary school in the 80s and I definitely didn't get English until I went to secondary school around the age of 12.
I do think the subtitling really helps with proficiency though. School can only teach you so much. Consider Ireland where people get taught the Irish language for 12 years and hardly speak it.
The understanding of different accents, slang, drunken conversation etc can only happen with exposure to native speakers. Content in the original language really helps with that.
So while what you're saying is technically true, a lot of shows were only subtitled instead of being dubbed, it is also factually false, that is not the main reason for the proficiency.