Possibly....I think the important thing about poly is that there are a full spectrum of options for each relationship, and that the people involved need to figure out what works best for them.
Problems occur when people can't agree and try to force a relationship to be something that doesn't work for everyone involved- like your wife does not want a sexual relationship with H. It's not fair to expect her to, but it shouldn't be a matter of either she has to have sex with H or all of you have to retreat to monogamy. It's hard to have 4 people all click together as a quad, but there are plenty of ways for 4 people to work well as part of a poly network. Maybe your wife and B could end up having a relationship, just them. Or maybe B could date you and your wife, and H will meet someone else who is more sexually compatible with him, and all 5 of you could hang out and play boardgames but have separate sexy times. Each relationship between 2 individuals is it's own unique blend of friendship, sex, & romance, and poly relationships are still relationships between 2 individuals, who are also in relationships with other individuals, and those relationships will interact and play off each other, but it's still a collection of unique individual relationships, not some kind of hive mind where everyone falls in love with everyone else at the same time and in the same way.