This has been studied to death. But just like soybean farmers in Idaho voting for tariffs on China it seems a category of urban renter is more wedded to ideology than self interest.
The Austin metro area's population is up [1][2]. Austin's GDP is up [3]. Migration per se doesn't explain a phenomenon that is robust across cities, countries and centuries.
[1] https://www.macrotrends.net/global-metrics/cities/22926/aust...
[2] https://en.wikipedia.org/wiki/Austin,_Texas#Demographics