In the not so distant future when the miners reward consists mainly of transaction fees...
... mining will probably be a very specialized task representing a small minority of the network. The greatest part of the nodes has no incentive to discriminate between the miners because that can only slow down the processing of their transactions.
It is possible that being a regular node will not be so easy when the bitcoin network has grown and a node needs to receive and forward thousands of transactions per second. So the only ones that will have the incentive to be full nodes will be the miners. And everybody else might be using a "light" client that does provide this functionality to the bitcoin network.
I have already addressed this concern.