Interesting, Steve.Steve, Thank you! You are correct. It's rare to see such Sweatbands on Soft and Stiff Felt Hats.
Here is a J.Hückel´s Söhne "Flexible" Homburg.
Johann Hückel´s Söhne - Hückel Hutfabrik Weilheim
germanaustrianhats.invisionzone.com
My understanding is, the white sweatbands on top hats are for formal evening wear.
Black sweats were for day/work wear.
White leather sweatbands on a Bowler are unusual, but might suggest the class changes in Europe during the 20s and 30s after WWI.