The point is living in 7 different homes for 30 years, means at the end your home is paid off and you have no rent. Of course that is ideal, most people extend their loan terms often.
As you said - that's ideal. The home people trade-up to is usually more expensive than the home they move from (not counting empty-nesters) and - ideally - there will be a myriad of factors that can help one finish paying off their new more-expensive home within the same timespan, like more income or selling at a profit. But those aren't necessarily givens, as they're determined by things like your locale and the state of the housing market.