Good points. What about if being polyamorous means “having a preference towards multiple/open relationships” rather than happening to have them? Just like being bi means being attracted to both sexes without necessarily requiring a relationship with one of each to be happy. And being straight doesn’t mean you aren’t happy single.
Personally I don’t have an identity to do with relationship structure, same as you. For me it’s because I can see myself happy in lots of different kinds of relationships, depending on the people/circumstances, and there’s no single word to cover all those.