I can relate to do much of what you said, although my STBXW was once a month to six weeks. I ended up leaving the marriage about 20 months ago. Your counselor is right about your choices; your husband is happy with this aspect of his life because he's getting his needs met just fine. So he doesn't see that there's a problem. Unfortunately, he's not seeing that your needs not being met is a problem. So your choice is learn to live with it, or leave.
FWIW, I've been seeing a wonderful woman since shortly after I separated. Not ideal, but we were both looking for a physical relationship after leaving essentially sexless marriages. A "no strings attached, you scratch mine, I'll scratch yours" type of thing. But we fell in love. And have been going strong for most of my separation. I think her record for no sex in her marriage was around 2 years. We've found we're very compatible sexually (daily is great!), and I think I've had about 10 years worth of "married sex" with her. And that's just talking quantity, not quality. There's not a hope of comparing quality...
I say this not to brag, but to let you know there is hope of finding someone new after a sexless marriage. I'm 45, and I'd consider myself nicely average looking. She's 42, and much prettier than I am handsome.

. The sexual connection we have has given us an incredible emotional connection as well. I just wish I hadn't spent the last 20 years merely "existing".
C
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