What if there were houses with a time limit on how long you could own them? When this time limit ended, you would resell the house and put it back up for auction. Optionally, you could pay for the house again (at a slightly inflated price) and keep it for another period (after this second period, you would not have the option of purchasing again). This increases house turnover, encourages some degree of exploration (if you keep moving, it increases the odds that your new home is in a different location), and increases the development on a home you rent. Time limits would be long enough to allow for development on property and "settling in", but short enough so that turnover remained relatively high. Limits could even vary with property, from a few days on "prestige" property to a month on others!
I would recommend that the majority of housing in high-traffic areas should be time-limited, and out-of-the-way housing would still be purchasable, similar to "vacation homes".
What would be the implications of this? Downsides?