Personally I do the exact opposite. I take out a loan with the highest possible ltv and find a property that cashflows. If it's making me money I don't care if there is a loan - let the tenants pay that off for me.
Any time I get too much equity in a house I'll use a heloc/cash out refi to get money to buy more properties. You should always think of your ROI per dollar invested. Paying down your loan will give you a 4% ROI (or whatever your interest rate is). The stock market will give you 8% typically. Leveraged real estate (continually buying cash flowing properties using loans) is closer to 20-25% CoC depending on the properties you buy.
**Quick description of your ROI after 10 years in each of those 3 scenarios assuming the $6k in contributions per year:
Pay down mortgage (4% ROI):
60k principal + $12k interest = $72k saved, all as equity tied up in home
No extra payment, invest in stock market (8%):
60k principal + $27k interest = $87k, all as liquid assets
No principal payment, buy more proprieties with mortgages (20%):
60k principal + $95k interest = 155k, paid as monthly income via rent
As others have said it depends on your risk tolerance but personally I'm going to take advantage of the cheap bank/govt money and grow my wealth at as fast a rate as possible. So far my two properties are each yielding >25% ROI.
I was doing the same thing as you two years ago until I realized I could get a better return in the market. This year I realized I could get a far better return in REI. I'm 28 now, I'm just investing from my salary - I intend to retire in 5 yrs.