I think it is a good sentiment! I know I have tonnes of base/inserts around that would probably make a kids day, but don't have anywhere to send them!
Maybe you could just have people in each state who are willing to be a holder or gatherer of donatable cards so that anytime someone does a deal with that person, they can send a few extra that they want to donate!
Then, every now and then, that 'gatherer' takes them to a hospital or donation centre of some sort!!
I remember doing something like that years ago when I began collecting, Dad and I used to give our spares to the local hospital. They were used to entertain and teach the sick children.
I am only too happy to help in any way I can with this.
I think once you find the charity/ies then its just about having a central point to collect the cards and send them on. There really should not be that much to it.