I decided to spot check a few, including places like Portland and Seattle, and it seems like private ownership by a family for the last century is pretty common. And isn't the main paper in Austin the Austin American-Statesman? That's the Hearst family. Though looking a little deeper, they were owned by Gannett until last year.

Yes for big cities, but there are very very few independent local papers in less populated areas, for example: https://www.portlandmercury.com/news/with-a-new-media-conglo...

Also the Oregonian (big Portland paper) and the Seattle Times (big Seattle paper) are not locally owned anymore.