As I recall, it was less supplanted, then “evolved from”. Those sombreros were less upturned than the modern stylized ones would lead you to believe. And rain could be easily be dealt with by pinning or molding up the sides of the brim. Basically creating a gutter.
This is why the brims of cowboy hats are typically upturned at the side. Also how you get the tricorn hat, which are basically just an at the time typical broad brimmed hat. Pinned up to channel rain.
It’s also why the umbrella hat is ridiculous. Is does nothing a whole hell of a lot of wide hats havn’t been doing for centuries.
