If I were the parent of a participant, I would worry that such a show would hurt the child's enjoyment. I also worry that participants and families might later wish to have kept some things more private than the show's producers will choose.
Would being televised in a skating context affect a USFSA skater's future eligibility to compete? (I assume USFSA hasn't sanctioned this, but could be wrong.)
Could the PSA sanction a coach as abusive as the Dance teacher in Dance Moms? See
http://www.skatepsa.com/Tenets-of-Professionalism.htm--
Incidentally, "Kids on Ice" is also the name of a charity-supported USFSA LTS program for kids 18 and under at Fort Dupont Ice Arena, in Washington, DC., which, BTW, has a new skating director.
The Fort Dupont KOI is nothing at all like Dance Moms. There is a moderately thick plastic shield between the ice rink and the parent's area, that it is hard for parents to be heard through (great idea!). if parents do complain, the skating director could offer a full refund - it's free.
But I will email that KOI skating director a copy of this notice, just for laughs.