He's obviously going to say that he wants to save the marriage, but this would be entirely for his own self interest, not for the wellbeing of his wife.
But his wife wants a marriage without sex. I don’t get the impression this is about sexual compatibility, but about the fact that she doesn’t really enjoy it and likely wouldn’t with anyone.
Realistically, she now has to make a decision about whether she wants a compromised marriage or no marriage at all. It’s not about whether he wants to “save his marriage”. That phrase has connotations of trying to get it back to some kind of normal, monogamous relationship including all aspects of a normal marriage, which for most would include sex.
It’s not about whether he wants to “save the marriage “ but about whether there are other values about the contract of being married that outweigh the romantic ideal that he might have the perfect future with someone else, if only he can find her,
He may have been playing OP all along. He might have been staying while getting the chance to play away with the full intention of leaving when he did. But he might not and he might not have the intention of leaving, even now.
I realise he is not considering the well-being of his wife and putting her first, as you would expect in a full, normal marriage situation, but this isn’t a full, normal marriage situation, and has no chance of being that.
As someone who has left her marriage because of certain behaviour patterns in my ex that I couldn’t live with and retain my self-respect, I am now 52 and looking at a long and probably quite lonely life. I miss things about my marriage, such as having a friend, doing things together and feeling that there was someone there when the chips were down. He was wonderful during a long period when I was very unwell, so the marriage was not without any value.
Had I been able to live with his actions and retain my self respect, while recognising that my marriage was never going to be properly “happily ever after” I could possibly have had a reasonably contented and comfortable old age.
Many of us live with compromised marriages, but that doesn’t play well with the modern version of the fairy tale, which says that if the marriage isn’t perfect, we should walk away and might find one that is. Maybe the OP will get lucky and find a man with no interest in sex, but I think it might be like trying to find a needle in a haystack.
Not so very long ago, leaving your marriage was unacceptable and compromised marriages were probably the norm. Doubtless some were very unhappy at being stuck, but others might at least have appreciated some aspects, such as knowing there was a degree of stability, even if it was imperfect.
I don’t think I’m being entirely naive. I think it’s possible I’m being ruthlessly pragmatic, but have a perspective that’s alien to current expectations. Maybe he’ll lie, maybe he won’t. OP might well be able to tell the difference, unless he’s a practiced liar, which the current situation suggests is not the case. If he was that, he could easily have accepted no sex and had affairs and lied and never told her at all. At least he came to her openly, explained that he wanted to continue the marriage, but that if she didn’t want sex, he needed some compromise.
He now wants her to compromise again. He hasn’t been completely honest about it on this occasion and that is the problem. Whether the further compromise can work for her is up to her. Maybe OP can’t live with it, maybe she can’t. The only way to find that out is by working through a process of discussion about possible ways it might work, if she decides that’s what she wants.
What she can never have again with this man is a relationship where he is putting her needs and well-being first in every situation. It’s up to her whether she can live with that fact or not. I’d say that up till now, she has been lying to herself about what this is. She hoped that was still a possibility, but as soon as he asked for an open marriage, that possibility was gone. She is now facing it, and of course it’s painful.
But I can’t say whether it’s worth it for her to try and persevere or not. She needs to work that one out for herself, bearing in mind that she has no control over his actions, but has to choose whether she is willing to accept this at all, along with some kind of assessment over whether she can still trust he’s telling the truth or not. She may decide it’s worth the risk, she may not, but only she can decide, and for that, she needs a cool enough head to look at this pragmatically and understand the actual choice she has to make,