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. They 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.
Why should those non-mining relays (NMRs) be assumed to be "good guys"?
The original bitcoin protocol (without NMRs) provided some guarantee for simple clients, under the hypothesis that there was a majority of selfish greedy miners, and that the miners contacted by a client included at least one selfish greedy one. With NMRs, in order to give the same guarantee one must also assume that there is at least one path of
honest NMRs between the client an such miner. The basic premise of bitcoin is that selfish greed is prevalent, but honesty cannot be assumed.