Miners can mine (produce block) and serve user content storage requests.
That's the nodes' job. Running a full node serves the network in two essential ways: It helps it bandwidth-wise, and it insures the presence of the chain in more places. Miners can right as well run a full node, providing extra storage, but their job is to provide computational power.
However, if the miners are keeping the content for the users, they will receive the payment for storage resource every week.
I think you've confused the purpose of running a full node yourself, and avoid trusting a third party for doing it for you. There's already an incentive on running a full node, that is privacy and security. There's no need to essentially tax the users who don't want to run a full node, which is what you do if you reward those who do run one.