I'm not a late learner. I'm exposed to English when I'm ~4 yo, and started to learn it at 7. Also, I cannot learn by mimicking. I listen and read to learn, to understand how the culture is choosing words, how it works in real world. It's a kind of practice.
Because of my Job, I'm talking with Europeans a lot, and I'm considered a very clearly speaking guy. I've some accent which is carried from my mother tongue, but not from mimicking English dialects.
My English education wasn't purely language education. Whole curriculum was in English, so there was no place for mimicking. We were forced to think in English. The language is integrated into our lives for 6+ years. As a result, I can write at the speed of speech. Also while initial spellings are given as complete words, pronunciation is taught to us. So I can reasonably read or speak a work I've never seen.
When I go abroad to attend some meetings, I cannot completely switch to my mother tongue (both in spoken voice and inner voice) when I land for 30 minutes or so.