Any reason why "De man schrijft nooit zulke brieven" is wrong?
It is correct. Starting with "zulke brieven" just puts more emphasis on the letters.
But is it really necessary to emphasize these "zulke briefen" in this case for a proper translation? I mean every is it like that that when I find somewhere such or similar English sentence, I have to translate it into Dutch this way and only this?
No, on the contrary. See my reply to samulili earlier this year. I'd never translate the English sentence by starting with "zulke brieven".
It is even more correct than the translation Duolingo suggests. For some reason it inverts the two sentences, whereas in other exercises it insists you use the same word order.
I am also lost sometimes with these confusing expectations about
the translation :)
Dergelijke brieven........ No good?
perfectly all right