Why don’t you do right?

Could you please tell me if the sentence ‘Why don’t you do right?’, which I’ve only heard in a song, is just another way of saying ‘Why don’t you do the right thing’?

Why don’t you do right
Like some other men do?
Why don’t you get out of here and
Bring me some money too?

Thanks, as ever, for your time.

Yes, it means, “Why don’t you do the right thing?” but it’s heard almost exclusively in songs. I suppose it’s said in some Southern US dialects, but to me it sounds like something I’d hear on a scratchy old 78 rpm record from the 1920s.

Maybe do it right also sounds a bit like get it right or get right with me which are probably slightly (or not so slightly?) different things? I remember these songs by Depeche Mode - “Get the balance right” and “Get right with me”.

“Do it right” (with “it”) does not sound archaic. It’s “why don’t you do right” (where “right” is the direct object, or else there is no direct object) that sounds odd and is generally confined to songs.