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Designed by men, for men: Why sex with robots does not have appeal among women
(english.elpais.com)
This is a most excellent place for technology news and articles.
What they need is emotional intimacy, but they can't get that because of crippling anxiety. You're not going to get emotional intimacy from a robot, and if you try, you run the very real risk of really adverse effects, like this or this.
That's why I suggested separating concerns. Keep the bot physical, and encourage real personal relationships in a low risk environment. There's always a chance a personal relationship develops into something more, whereas there's a lot of risk expecting a bot to fill that gap.