How often do you use the word "for" as a synonym to "because of"? Never. Well, not unless I'm quoting the Bible or 19th-century poetry, for example. Is it common in nowadays? No. It is not used in modern everyday English. or is it AN archaic form? Yes, it could be considered archaic. If you tried to use it in an essay, for example, your teacher would probably tell you to replace it with 'because'.

It is archaic.

There is a certain use which I would say is old-fashioned rather than archaic. “I can’t walk for the pain in my knees” is something I wouldn’t say but my grandmother would have. There are other current uses of “for” which could be translated as “because of” though. I’m here for my wife. (Could mean I’m here to take the place of my wife, or to do something to benefit her. But you could also use it more vaguely and in that case a good alternative would be “I’m here because of my wife.”)