The real problem isn't a problem of vacant units, it's a problem of unbuilt units.
When you say "This results in a transient population," I'm not sure exactly what you mean by "this" but perhaps it's renting at all? If so, the only reason renting leads to "transient" population is the rising rents and displacement caused by lack of building.
> There is no lack of building
Putting something in italics doesn't make it true. In the vast majority of high demand areas, there's a smal smattering of new construction, far far less than comes close to meeting population demand, and locals freak out about the construction and vastly overestimate the amount. If your particular location is building 3%-5% more units per year, great, but most of the country is not and that means that every other place that's under building is displacing it's residents to where you live, easily swamping whatever you call "more than natural population growth"
This is exactly what buy to let landlords are doing.