I can see both sides. Without a catastrophic depression, more leverage (in real estate anyway) over decades will cause you to end up with far more assets and income than focusing on paying off the primary and a couple other properties. At the same time, having a nearly non-existent payment on a primary would enable you to live indefinitely (in a relatively nice place) on menial labor jobs alone, which a big mortgage would not allow. I won’t be sitting around sending out tech résumés for 7 years – I’ll be at the unemployment office asking for temp ditch digging or gas station work. When the entirely leveraged guy runs out of money in 10 years, he’ll be going home to the rented room (or 2-bedroom with roommate) that his minimum wage job permits.
Once our passive income is at a point where retirement is possible, we’ll start putting a lot of extra cash toward the primary.