It needs to be such a rapid swing that that the costs of renting (including rising rents and losing out on the MI deduction) are more than offset by the increased affordability (i.e., house prices combined with interest rates) of homeownership.

Again, the only time these variable lined up in such a way for the practice to make sense from a purely economic standpoint was if you sold a house that you had lived in for more than 3-5 years (depending on your equity at the time of sale) from the fall of 2005 until the spring of 2007, and then rented until the spring of 2011 until the summer of 2013. That's a pretty narrow window, especially for an unprecedented economic environment that nobody really knew how long it would last.

Talking about Utah, if you sold before then and rented longer, any potential gains would likely be eaten up by the costs of renting, the loss of additional [bubble-inflated] equity, and the loss of the MI deduction. If you sold after that, it would have been after the bubble popped. If you rented for a shorter period of time, and bought in, say '08, '09, or '10, you would have still suffered loss of value on the second home your purchased a home values continued to decline--a lot of people fell into this with the refundable and non-refundable first-time homebuyer credit. If you waited longer, you would have bought when home prices were on the upswing and with low interest rates, but the longer you rented the more you would have been subject to increasing rents (which, during that period, were rising as fast or faster than house prices) and the loss of the MI deduction.

I guess I'm saying that it's possible to pull off the kind of strategy you're talking about; it's just extremely difficult. That being said, there are other non-economic reasons why it might make sense to rent for a bit before making a secondary purchase. You want to feel out neighborhoods, try out schools, ward hop, not be tied down to a location, etc. Those all make sense, and are perfectly defensible. But for most run-of-the mill "I'm selling my current house and looking to buy a new one", I think most people are better off playing it pretty straightforward and buying based on their subjective criteria of affordability, and not trying to game macroeconomic conditions.