Not entirely convinced as this is a description of changes which are quite specific to the US and the usage of hats went out of fashion everywhere.

Perhaps if one can date different dates of decline for hat usage across different countries in relation to prevalence of automobile usage.

However I remember very well that my grandfather in the 1980s always wore a hat while driving his car. In fact he specifically put his hat on to drive. And at least in Norway old guys driving with a hat is kind of a cliché.

To me it seem more like the whole fashion changed. Everyting became more informal. People did not just stop using a hat. They also stopped wearing suits all the time.

Hat usage disappeared primarily in the 1970s in Norway, and that is also when people stopped wearing suits to work.Suits only got worn on special ocassions.