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.
Non-mining relay nodes have several useful purposes: probably the most important one is as a first line of defense against denial of service attacks. Especially if such nodes are run in the cloud service provider who charges $0/GB for incoming traffic (like Amazon EC2): it nearly completely defangs the most common DDoS via UDP flood.
I have to observe that for somebody with an actual scientific degree you are making questionable statements too fast and too often.