I generally refer to this type of breastplate as a "hunter breastplate," but in truth, you don't see a lot of breastplates at a hunter show. In fact, a quick scan of my hunter show pictures revealed lots and lots of standing martingales but not one single breastplate.
Despite that, I don't mind seeing a model hunter dressed up in a breastplate. They're not illegal, just somewhat out of fashion. You do see them occasionally at hunter shows--sometimes because of a saddle fitting problem but other times because the owner "just likes the way they look." I totally understand that sentiment. I like the way they look, too!