This would just increase the digital divide, people with a poor internet connection and little hard drive space to spare would not be able to participate.
One of the nice things about bitcoin is its accessibility, an impoverished farmer can walk into a dilapidated shed, connect to the dial up connection with the crash-prone 2003 computer, and spend his hard-earned milli-bitcoins on a sack of grain.
Requiring users to run a node would turn bitcoin into an elitist system that can only be used by people with fancy computers, fast connections and large hard drives.
My PoN idea gives a privilege to node runners, but still lets others use the system, they just have to wait for their turn while the node-runners skip to the front of the line.
I thought the argument against this was "Moores Law means technology will be dirt cheap"? At least that was what everyone keeps saying.
However. I have hinted at a distributed block chain that would mean an on-disk size less than 1GB regardless of chain size meaning the concept of a full node as one that has to have the entire chain is irrelevant.