Nope, unless shiny is your goal. If I have to, I can play on just about any horn or mouthpiece. They together create a system that can be logical or problematic. This type of question does not come up among reasonably developed players. In this particular case, the merit of a flugel mouthpiece on a trumpet was compared to owning a flugelhorn with a matching mouthpiece. In real life, you can do anything you want to - in your bedroom, but getting jobs means work not play.