You need to shop carriers, this is a non issue.

I'd send an email to my agent notifying him of the change in risk and keep that email as evidence that I notified the carrier in the event of a claim.  

Insurance brokers still give bulk discounts, even if the one client has policies with multiple carriers. 

Meaning that the insurance carrier is required to pay you the limit stated on your policy, no matter what you have invested into the policy.So if you bought for $100k, invested $50k,  insured for $200k, then had a total loss, the insurance carrier would need to pay you $200k.Your statement is correct in states that are not "Policy Value" states. 

For the not-so-big-one like you say, I'm guessing most of the damage will be on me, not the carrier.

On standard for 401, there is a section instructing the owner to carry general liability insurance in the amount of $XXX,XXX, but it does instruct them to consult their insurance carrier. 

@Tony Reynolds first of all @Brandon Carriere is right about Zestimates - so ignore that.

Putting their info on it and leaning it on the door just like the mail carriers would.

It is going to get worse, plus the carriers are aggressively fighting it. 

Carriers are stopping writing new business in certain areas or stopping completely2.