If a relay doesn't accept posts from random pubkeys (usually for spam prevention purposes).... how could gossip test that it would work well as an inbox?   I can't create new events signed by your friends.  Best I can do is make up a random keypair which will get rejected.   Basically I think inbox suitability cannot be tested on such relays.  Gossip will give such relays an X for inbox usage because I have no way to otherwise know, but the (OK, false, msg) message will be available as a hover-popup to users so that relays have a chance to explain themselves.