Christopher

The Forum you posted in can be exclusively answered by Steven Long. While it is definitely legal by Rules as Written (RAW), it is marked as having "great abuse potential": " If a power with Continuing Charges is bought
through a Multipower or VPP, and the character
switches the Framework to another slot afer using
a Continuing Charge, the Continuing Charge does
not immediately turn off. It continues to affect the
target or area until its duration expires. Te GM
should examine Continuing Charges in Multipowers carefully to ensure that they don’t unbalance
the game. For example, a character shouldn’t be
allowed to buy a Framework with several slots
that have lengthy Continuing Charges just so he
can activate all the powers at the beginning of the
game and have them remain in effect for a long
time"
There are two markers with many powers: Exclamation Mark and Stop Sign. Exclamation Mark means it has potentially problematic cases. Stop sign means it is extremely likely to break your game if given to players. I would say this use of Continuing Charges would be a Exclamation Mark case.
So you would certainly be in your right as GM to disallow it.