If there is no damage from a forced entry, it is a lot harder to get a claim through. Mike Wendland mentioned that.
If I have to store my rig in a high crime area, I'd leave things latched (but unlocked), notes stating that, and a dud TV or laptop in one of the bays. That way, the local tweakers get off with something, and don't trash the rig.
However, since I store my rig well out of the city limits, it stays locked. I lock the doors, storage compartment, and have locks (security chains + ABUS padlocks) for the wheels, as well as a "token" hitch lock just to show a would-be thief the rig isn't theirs. This helps with theft of the vehicle.
Now, burglary is a different story. I leave things locked and park my rig miles from a paved road just because I don't feel like surrendering and letting the meth-heads have their own "pick and pull" of their own choosing. Since cars and RVs are easy targets (just smash the glass), the only real method of defense is strongboxes that are well bolted down. For example, ConsoleVault for the middle compartment, and a Tuffy under rear seat lockbox for under the seat. Since it will take a good amount of time with hand tools to get past those, it helps keep the valuable stuff away from the smash/grabbers.
In general, if it is lockable, I lock it. Just old habit from growing up when Austin's economy was in the dumps, and if it wasn't not just bolted, but welded down, it was gone.