There is a mindset that why pay off the mortgage early, it's a tax deduction right? Well, if it's so great, why don't people ask to pay a higher interest rates? Have you ever hear people say, tax me more please, tax me now!!!
Even if you're interest rate is 4%, you're not really deducting the whole 4% dollar wise when you do your taxes.
Yes, having to pay taxes on you're income on a free and clear property sucks, but you will cash flow more of course and it will allow you to buy more properties.
That said, if I had one million dollars and each home was say $100k. I could either choose to buy 10 homes cash or put 25% down on each and buy 40, I would choose to buy 40 because of the appreciation potential, but I would at least cash flow $200 - $300.
A 15 year loan on $75k @ 4%, PITI is about $800. I can get $1000 on rental in my area. If you rather get more cash flow, then put more $ down, but I'm good with those numbers.
So, let's assume that in 15 years, the homes will have doubles.
Person #1 - Paid all cash for 10 homes.
Home Net $2M+ $1,800,000 on cash flow. ($1k * 10 * 12 *15)
Person #2 - Put 25% down for 40 homes.
Home Net $8M + 1,440,000 cash flow ($200 * 40 * 12 * 15)
Who would you rather be? Sure it's more work and I make it sound easy when I know it's not, but you get the idea. I'm sure I'm missing details like taxes, repairs, vacancy, aliens from Mars landing, blah, blah, blah. :)
As far as being sued because you don't have 100% equity, people can sue for you anything, just because you only have 20% equity or whatever, doesn't mean they can't come after you. Get an LLC, S-LLC (Some States), Land Trust, Umbrella Policy, etc.