These shoes were seen as being typical of the sort of footware likely to be worn by the kind of lounge-lizard who might persuade one's wife to spend the afternoon in an hotel with him! In other words, be a typical "co-respondent" sort of man.
When I was corresponding with my pen-pal in China, I always used put my corresponents shoes on first. It does really help you think - that is probably how they got their name.
I have always been in two minds whether my never-ending postings on this site over the past 84 years count as corresponding but so far I have never out my special shoes on. I always wear my pinkle-whickers.