That’s true. In Dragnet, usually before they learn of the episode’s assignment there is some of that dialog about their personal lives between Friday and his sidekick. Friday typically gets impatient with the sidekick, who takes too long to get to the point, and it’s always the sidekick who initiates it; Friday rarely talks about his personal life, unless asked. The idea is to show that Friday is all about business.
And yes, generally speaking, that’s the way people really talk (I should know, my masters is in discourse analysis. I study this kind of language in real life contexts.) However, in Dragnet they just tried too hard. It was so contrived, that after a dozen or so episodes it loses its effect. Still, it was better (and more realistic) than the typical dialog of most of the stuff on those old shows.