The bowler hat is a hard felt hat with a rounded crown created for Thomas Coke, 2nd Earl of Leicester of Holkham, in 1850. It was designed by the hatters James and George Lock of Mr. Lock of St. James's Street and was dubbed by them early on as the "iron hat".

It was the traditional headwear of London city 'gents' and has become something of an English cultural icon. However English men stopped wearing hats as a matter of course in the 1960s, and most young English people in the 21st century have never seen a bowler hat worn as part of normal dress.

In the United States, this hat is also known as a derby hat.

derbies - type of shoes .

First of all, one word is missing in the text above. It should read:

"Perhaps we should START wearing derbies."

Ref: http://www.onegoodturntent.org/newsletters/0512.pdf

Next, David and Cristina have given meaning of "derby". From these two answers, we can learn that derby is a thing of the past.

Because in the text the speaker complained about non-existence of true marriages in these modern days, then by "wearing derbies", he may refer to getting back to old values of marriage (like loyalty of the wife, the man is the sole breadwinner and so on) so that true marriage can be achieved.