As far as I can recall, this is the first I've heard of the word "fain". I think it just might be archaic. Oxford indicates that it is archaic. I'll have to make it part of my daily speaking. I would be fain to do so. Actually, I'm just "feigning".
I am not familiar with the development of the English language but with German. Similar movements took place. Talking to older people or people in rather isolated regions (oh, yes, they are still there in the middle of Europe) shows some rather interesting speech patterns.