And yet, I'm sure there's some way to learn pronunciation well.

I worked with a woman that was born in India, learned English with a British accent, and then learned American English and lives in the US.

The first time she switched to British accent I was gobsmacked. Then she switched to her native language (I don't remember which) and she clearly had a native accent fro that.

And then she switched back to US accent and I couldn't tell it wasn't native, too.

How did she learn? I wish I had asked her. It just seemed rude to ask at the time. She was very nice and obviously trusted us enough to show her accents, so it probably would have been fine to ask. Oh well.