It's important to know that the insurance industry is moving towards covering catastrophic events only.  

It weighs on my mind that my situation isn't more diversified and subject to such a potentially catastrophic risk.

In addition, keep in mind that the deductibles are usually quite high so the coverage available really qualifies as catastrophic coverage.   

But in the case of disaster or catastrophic loss, the rebuild costs of an older home can be a lot higher than that of a recent home.

Leaks can be catastrophic!

Personally, I believe that insurance should be for catastrophic life altering events.

Homeowner's insurance is most efficient when used for catastrophic loss.

So if something happens within the property owned by the LLC, in a catastrophic law suit, the most they can get is the property (Unless you screw up your LLC by commingling money, failing to maintain the company veil, etc...).Regarding outside liability protection (if something is happening in your life and you are sued for it), some states have better protection than others.

I have read that you shouldn't make any claims on insurance unless its catastrophic to keep costs down.  

Someone will know who you are and if a lawsuit is brought against your entities because of some catastrophic loss, it is not likely that you will be able to avoid discovery of where the true ownership lies.