After Pesach Chametz

Chametz שעבר עליו הפסח is prohibited due to a קנס.  The halacha (448:3) is that it is prohibited to everyone even to benefit from the chametz. However, there are Rishonim that hold it is only prohibited for the one who keeps the chametz and those that hold it is not prohibited בהנאה (see beginning of shiur of Rav Asher Weiss.)  

The Pri Migadim (434:9) says that chametz owned by kids would not be prohibited after Pesach since the קנס on chametz שעבר עליו הפסח would not be imposed on kids. In the פתיחה כוללת he is unsure about this halacha.

All of these issues may hinge on the geder of the קנס of the Chachamim.  Did the Chachamim place  an issur on the cheftzah of chametz that was kept over Pesach as an extension of the issur of chametz and if so it is across the board and carries all the stringencies of chametz on Pesach.  Or it is an issur on the gavra for violating the issur and if so it can have it may only apply to the one who kept the chametz and may only carry an issur achilah or may not apply to kids.  (We can sharpen the chakirah more and even if it is an issur cheftzah, is it an extension of the issur chametz with all of its laws or is it an new issur and may not carry an issur hanah (like the Briskor Rav's difference between the issur chametz Erev Pesach in the fifth hour or the sixth hour.)