@Jay Hinrichs. I am a brand new member so complete newbie to real estate investing so forgive my jumping in on a topic you are probably already all over. However, I am a 20 year insurance agent who has done lots of property and liability. For the past 12 years I have specialized in doing construction insurance for real estate developers doing projects 10M and up to over $1B and doing what is called OCIPs (Owner Controlled Insurance Programs).
Just my two cents but if you have multiple properties you might look at a commercial package policy that may have the option of blanketing property (one limit covers all properties and contents assuming they are not all in same location as carriers dont like that). May be cheaper and give better coverage for less premium because the likelihood of all properties being damaged at same time is highly unlikely.
Self insurance if done correctly is regulated by each state and you may need some help in order to do it. If you're just talking putting money aside in the event of a loss with no insurance that is up to you but I doubt any lenders would allow that unless you own outright and can do as you choose.
Just a heads up to all we are at the beginning of a hardening property market so expect rate increases that are not pretty. The carriers that do business property are different than those who do one off residential and may provide more appropriate coverage for investors with multiple units.