Hi Inky! Don’t you think that is pretty tough? Shouldn’t his wife decide for herself whether the FB-Account is important for her? Where is the border? You could also argue that talking on the phone, writing messages or meeting with other people is not necessary…
Controlling someone else does not help to fight the feelings, and you actually will never be really satisfied but just go on to try and control more and more… This does not create trust, but undermines it in my opinion.
It happened to a friend of mine, who tried to calm her boyfriends fears and jealousy all the time. They broke up because he still couldn’t take it and tried to control her whole life, while she became more and more isolated. I think you cannot live without trust in a relationship.

I think that you are right that social media encourages a lot of stupid stuff, but his wife has already laid open her account – which I think is a very strong gesture and shows that she uses it thoughtfully. Asking her to delete it would somehow diminish that gesture.
However, that’s just what I think… and I am myself in the position of the person who is jealous.