I don't think it was necessary or appropriate for them to move in together. Both are rather traditional that way, and I think living together after they were married seemed to fit DM best, and maybe LG, too, being the head teacher at school. After all, it may indeed be that DM didn't feel comfortable having sex without a clear sense of deep commitment between them. He had intimacy issues, absolutely, but it also seemed that he wanted real commitment before having sex, which is old fashioned, indeed, but also kind of sweet.
I agree that DM is a traditional man -- as is Louisa -- but I'm not sure that living together after an engagement was out of their comfort zone, but rather that they actually don't know each other very well. Whatever decision a couple makes -- to live together, not live together -- is fine, as long as they actually talk about it. But I get the sense that the lack of communication between them is a key component of their problems. They both need to be able to say what they want/need -- and not be afraid that expressing it means the end of the relationship.
I assume it is deliberate by the writers that it is Louisa who 90+% of the time is the one who initiates a physical gesture of intimacy. She kisses him first in the cab, she talks about seducing him, she grabs his hand when they are outside the surgery doors in the Peter Cronk episode. She grabs him for a passionate kiss while in labor.
It's not to say that Martin doesn't want and enjoy sex with Louisa -- but he is clearly waiting for her to take the lead. Perhaps when he feels more comfortable and assured about the relationship, we'll see a bolder Martin -- sure hope so