I don't know why people only care about the size of the opening of a mouthpiece when they're shopping for one. Of course, the size of the opening is important. Larger tips are better than smaller tips. But this is only one factor that affects how well a mouthpiece works. Other factors are the baffle, the chamber and the facing curve. The mouthpiece has to be shaped correctly. If not, it's going to be difficult to play and the player won't have as much flexibility with the notes.
The other issue that I see is that players think that they can play better or achieve a specific sound simply by changing the mouthpiece. But that's not true. Technique is what's important in achieving sound, not the mouthpiece. The mouthpiece can't make anyone play better. So just because you have a tenor saxophone mouthpiece doesn't mean that you will play tenor well.