As for the non-mining relay nodes, they are aberrations that have no place in the protocol and break all its (already weak) security guarantees. Thhey should not exist, and clients shoud not use them.
They actually provide a great deal of value to the network. They keep miners honest by checking blocks for validity, and *not* relaying those which are totally invalid, or make coins up out of the air. If you make a block paying yourself with invalid proof of work, it won't get further than the nodes you announce it to.
Care to explain your position on why they are not to be trusted?