For some they are the best of both worlds; the 'airy' lather from badgers and the backbone to tackle the hardest soaps. For others they are just not what a 'pure' brush of either kind will give you. But since you asked why don't you try one? They are not very expensive and good allrounders. A cheap and decent, but small, brush is the Vulfix #10.
The downside of the mixed brushes for me is that the grade of badger hair in those is usually pretty basic so they stay a bit prickly. But for the money they are not bad at all; if you like them or not, or add something to your collection is just another YMMV.
I must to the barber's, monsieur, for methinks I am marvellous hairy about the face