We've recently had a thread about My Way, which was rewritten by the aptly named Paul Anka from quite a good French Song.
That wasn't a translation, it was a completely new (and as it happened vastly inferior) new song, using the tune.
My impression is that most so called translations of songs are in fact more like that. There's nothing wrong in my view with doing that either. But a true translation is in some ways much more interesting - and it is a lot harder.
One problem is that songs tend to be full of references to other songs, and you get place names and so forth which have meaning that just can't be translated. So any translation that is going to have then same kind of overtones is likely to have to be a bit of a rewrite as well.
I tried doing a translation/rewrite of a French chanson which I really liked, and wanted to be able to sing, with special contemporary relevance. Just for interest here is the original, Les loups sont entrés dans Paris , and here is my version, The Wolves are on the street.