As I understand it, most other languages have a much shorter list of words that are specifically taboo for anyone to say, in a polite context.

Well, you understand wrong.

But we English speakers have this lovely category of words that are both nominally “forbidden,” yet also used all the time, by almost everyone.

Please don't attempt to make these kinds of linguist generalisations when you have next to no knowledge about anything else but your native language. Again, this is not exceptional to English at all.