OK, those are your opinions, I have mine.
If you haven't seen the show, the puppets are on sticks and generally held above the actors' heads. The puppets are roughly the size of a kite, so they sometimes hide the people, or at least their heads. And the puppets have working mouths that the actors move in synch with the actors' voices.
Dropping them to sing the last few lines isn't going to make me lose sleep or anything. My opinion is that doing so doesn't make the story any deeper - it does however, bring attention to the actors (who deserve it) but at the expense of saying "that wasn't really Nemo." Again, it is merely my opinion that such a high quality show, especially one for so many children, could have found some other way to highlight that ending.
And to that end, I think the comparison to Mickey taking off his head is valid. I know there is someone underneath there - I appreciate their efforts dealing with kids and heat - and I show my appreciation by thanking Mickey and not 'breaking character' while my kids are there. The Nemo show does that break and I just don't see why.
I thoroughly enjoyed the whole show, including that part. I can guarantee Disney really thought hard about that drop, and I'm fine if they leave it in (not that it matters

). I just thought to myself as I left the theatre "I wouldn't be wishing they dropped the puppets if they hadn't - so why did they?"
My wife teaches theatre, so of course we conferred. She liked the Broadway aspect of that ending and thought that overall that show was fabulous. She found errors I didn't, but that's to be expected. I too thought it was fabulous but again, kind of wondered if Disney wasn't sacrificing too much from the kids aspect for the sake of adult sophistication.