I just want to add a little perspective to this discussion.
Let's pretend that the Bb trumpet is a "piccolo trombone." It IS one octave higher, just like the piccolo trumpet is an octave higher than the Bb.
Now conventional wisdom suggests that one develop technique on a Bb trumpet before moving to a piccolo in order to establish the basic skills and not "epic fail" on the piccolo.
So before playing a piccolo trombone (remember, a Bb trumpet), shouldn't one start on the trombone? To develop technique and not "epic fail" on the piccolo (trombone)?
No, that's different, you say. But don't forget the experiment Arnold Jacbos did where he found that the pressure/flow ratios for all the brass instruments lie on the same curve, intersecting on enharmonic notes.
Finally - most rank beginners experience something akin to an "epic fail" on Bb trumpet when they first pick it up. We're just used to sounding OK on picc the first time because we're trumpet players. If he wants to start on picc, he could. And he'll eventually develop piccolo technique and perhaps become quite good. But he won't develop the rest of his register - just like I can't play trombone. Even though I play piccolo trombone rather well.