I was wondering about this for a token concept. Like, could one create a token that would be distributed randomly to anybody running a node and the length of time they run that node continuously.
For an actual blockchain, I think the short answer is no. There is no "Proof of Running a Full Node" concept where a proper economic incentive could be established, but maybe someone will come up with it. The one problem with rewarding full nodes for keeping a full account would be verifying that they are in fact running a full node. How can the network in general be assured that someone is running a full node without checking all that data that is the full node? Its easy to prove work was done to mine a block (you just check block hash), takes no time at all. How much time and bandwith would it take to verify full nodes? I have to imagine it would be a lot.
The real advantage to funning a full node is having a higher degree of security for transaction reliability.
On another note, in the future if there does emerge a "bandwith currency/token" there may be built in economic incentive to running a full node because light nodes would constantly have to be re-downloading the info for specific blocks with specific transactions over and over again.
Just my two cents.