I feel for you, Rootlet. It sounds like your situation is more dire than mine. My husband at least enjoys sex -I never get the impression that he is going through the motions for my sake. I guess an analogy might be a chocolate truffle. He'll happily eat one if offered, but is not spending any time longing for truffles, missing truffles, making time to go buy truffles, or eagerly awaiting the next time he gets to enjoy one. For me, sex is a lot more central to my life, and so is romance.
We still have plenty holding us together, not the least being our shared love for our two daughters. There's still no one else in the world I'd rather be married to. We share some interests, although we spend less time on them together than we used to. (I've been unhealthy for 6 months, which is really a contributing factor to our overall marital frustration.) I wouldn't throw in the towel over this.
Sex therapy would horrify him. Marriage counseling has been a hard sell, and he has finally agreed, although we haven't started. I do tell him what I like/want/need, but he claims he just can't flirt and never has. He has become expert at touching me in all the ways that I like once we are into it, but it's the in between, when daily life just sucks the intimacy right out of him, and I don't feel like we're close. He's willing to work on it. It's just that it's been a problem for 9 of our 12 yrs of marriage, and I've been bringing it up off and on for at least the past 7. It doesn't feel like we get anywhere.
It's sad, because I get the sense the healthy polyamorous relationships I read about don't involve bringing in another partner to make up for shortcomings with the first partner. I already feel like I "use" these men to put me in the mood for sex at home, which isn't fair to them, especially since neither of them have women to have sex with in their lives right now. On the other hand, if your spouse doesn't like camping/knitting/tennis, it makes sense to find other people to do those things with. My man doesn't like flirting.
There is clearly no simple answer.