Watch this Jean Carroll video from the same period:
Or Joan Rivers:
I’m not an expert on comedy history either, but standup has some roots in burlesque. A lot of what we think of as stand-up history (including the two clips above) is filtered by being broadcast on television (particularly the Ed Sullivan show), so the racier bits weren’t included. But Lenny Bruce and Mort Stohl are real comics who appear as characters on Mrs. Maisel performing their actual routines. And, as you can see above, a discursive (or even elliptical, ala Bruce) style was perfectly normal for period comics. Not all of it was Bob Hope delivering one-liners and Jack Benny doing double-takes for the audience.