You're right, I was confusing "abstract base class" with "interface role".
in reply to Re^7: Moose role with requirement consuming another role
in thread Moose role with requirement consuming another role
That documentation mainly talks about interface roles, but in the sentence "Because the role defines the required methods directly, adding a base class to the mix would not achieve anything" presumably refers to the fact that class<-(role or abstract class)<-interface-role won't work if you only meet your interface-role requirements in the child class. "base class" in that sentence should probably be "abstract class or role". The document is really warning that you should instead use class<-interface-role plus class<-(role or abstract class).
Now if I've understood that correctly, it's still a not explaining the behavior which I'm seeing. If both has and with are evaluated at runtime and not compile-time, putting them in the correct order should mean that a role can fulfill requirements set by another role, with either a subroutine or a Moose attribute, and not only with a subroutine. I don't care that we veered off-topic, because this taught me something, so thanks!