Some accent experts share the same point of view with you.

They'd prefer to teach those who can express themselves and understand others well.

I don't know which is the more effcient way in the end, if we want both the expressing skills and a decent accent. Learning "words and expressions" is relatively easier than reducing accent, but it is more time consuming than I wished earlier. The good thing is as long as we are working on either of them, we are improving.