First, the “Why”, because that’s the point I really want to make. In a word: CLARITY.
It seems to me there are many ways of explaining this. An example is perhaps best: Play a bebop tune as fast as you can, on the double horn. Then play the exact same thing on the F alto horn (descant or triple). Which do you think sounds clearer / more intelligible / listenable?
Another reason which is applicable to those who played trumpet before they played horn: It feels familiar. You relate to the instrument in a similar way: range / register / fingerings; although it in a different key.
There is some great information for John Ericson here: http://hornmatters.com/2012/10/playing-descant-and-triple-horns-a-new-e-book/
And, I’ve recently recorded an e-lesson for https://vimeo.com/hipbonemusic/vod which should be available around September or so. Check it out!