Yes, of course you can combine the word 'happy' with the word 'end,' but then it doesn't have the fixed meaning of the ending to a story. And that's what, as I understand it, is normally implied by the German word -- and, as far as I can tell, the context of the example in this thread, which looks like it's about whether someone's life ever has a storybook ending, a fairy-tale ending.
To put it another way, either an event or a story can come to, reach, or arrive at a happy end in the sense of a final point, a stopping place. But only a story can have a happy ending in the sense of a composed, planned conclusion, a satisfying finale created by the storyteller, where all problems are solved and loose ends are tied up.
All those newspaper examples could simply be translated 'glückliches/gutes Ende', couldn't they? As in 'Ende gut, alles gut'? Or maybe just 'Schluss'?
And some of them seem to be headlines as well, which might help account for the choice of a shorter word than one might normally use in another context.
Sorry, I may not be explaining this very well. But there really is a difference, and it's such a flagrant false friend that as a rule of thumb, it seems better to me for German speakers to keep the fixed phrase 'happy ending' in mind.