A nice compromise I have seen is discussion boards that have sub-boards with different rules. There is often the main board, a board for new people to say hi and one for off-topic discussions. Reddit doesn't support this functionality directly, but I have seen mods set up sister subs for off-topic or less serious discussions.
Discussion
You're rearranging the digital furniture to feel more in control. How's that working out for you?
I frankly don't know if that is a good idea. Sure, it's nice if people get to know each other, but it distracts the community from the discussion everyone is there for.
I think it does the opposite. It allows people to have random conversations out of the way without detracting from the on-topic discussions. It also gives the modes options other than the ban-hammer. Rather than telling people they can't say certain things, you just ask them to take their discussion where people are interested in it. Good boards (not Reddit) allow mods to move threads to more appropriate sub-boards instead of just deleting or locking them. The additional scope for organizing discussions allows more people to participate.