Is it okay for married people to keep in touch with people they were sexually and emotionally attached to?

My husband and I have discussed this on more than one occasion. I completely trust him and I'm positive he is honest and that he adores me as I do him. There's only one problem. I am more experienced in relationships than him. He is a bit naive and he does not realize it. He has never cheated or been cheated on to his knowledge. He has never fell victim to or been witness to the outrageous things that happen between people like cousins, best friends, fathers and, mothers stealing your significant other. He thinks it's completely unrealistic for a superior at work to be attracted to their younger counterpart. Let's just say my eyes are bit mre open than his. That being said, he thinks that just because HE has good intentions, other people do as well. He and I were very close friends before we began dating and he expressed to me that he no longer had feelings for his ex. He had no reason to lie because neither of us thought twice about being together back then. the more we hung out and became intimate, the more I noticed she couldn't let go. He's an easy going faithful and loyal friend. The type that won't abandon you if you ever need help so he doesn't just write people off. Being that he didnt feel for her and it had been 2 years since they were together, he was dating again but remained her friend. On the other hand, judging by her texts and her comments, she noticed a significant change in the dynamic of their "friendship" once he started dating me. She realized he was finally getting serious with someone and he wasn't as available to her as he had been in the past. When we made it official and made our relationship public, she continued to instant message him to "test the waters" telling old inside jokes and reminiscing about the past. Being, in my opinion, flirty and making sure lines of communication were still open. He didnt hide this or respond to her in a way that would lead her to believe he was still interested in her but he also didnt see what I saw. She was trying to make sure she still had a place in his life just in case something went wrong with us. She still misses him and can't believe he is with me, now married, and with a son on the way. He doesn't get how a woman works nor does he realize that the more he leaves his self open the more vulnerable he can become. He is only human and even if he never intended to fall prey to her, he still could be manipulated by her sneakiness. She was his first serious relationship. They were high school sweethearts. I told him how I felt and that he should tell her it's not appropriate for her to continue contacting him since he has a family and is no longer single. He didn't object but he hasn't had the opportunity to tell her because she hasn't yet contacted him again. She is still his Facebook friend and still comments and likes photos he's tagged in and so on. I've deleted all my ex lovers and flings from Facebook because I feel they no longer have a place in my life. He doesn't see them as a threat and I would never force him because it only makes things worse. He is not holding on to her, he still has emails from prospective jobs from 3 years ago. Hes just a pack rat and doesnt do things like erase old phone numbers and delete old friends. He is not the issue. I just want to know if I'm wrong for wanting him to cut all ties to should-be meaningless relationships like I do.