I don't understand an investment strategy of having all properties paid off. That strategy will greatly slow your ability to acquire more properties and increase your passive income. If you were to take a 75% LTV mortgage on your three properties and invest those funds into six or seven more income properties your passive income will increase tremendously. If your present properties do not have strong positive cash flow with a 75% mortgage then those properties don't make sense as investments.
Now let's move on to the next good reason to leverage those properties. Let's say your three properties are presently worth $100,000 each and they appreciate 3% this year. That would earn you $9,000 in additional equity, not bad!
Now let's say you leveraged those three properties and now you have a total of ten. If those ten appreciate 3% then you have earned $30,000 in equity! Wait, we're not finished yet. Now you take that additional $30,000 in equity and make a down payment on property number 11. The year after that if the 3% appreciation rate continues you will have another $33,900 in equity!
Now you are growing your real estate empire, increasing your cash, increasing your equity AND the leverage reduces the target for all those lawsuit risks that made you look at umbrella insurance.
Rock ON!