There are a surprising number of people that want things open these days. Some see the damages that can be from closing down to one person, usually because one person hurt them so deeply in the past. He may never change this outlook, but if that's not how you need things, you should tell him.
I've been very hurt, and I'm thinking I can't be in a one-to-one commitment again. I'm bipolar and have never cheated except when it was to break up with a cheater because I knew she'd find out.
If you're ok with accepting a "whatever" relationship status, then it could be good.