.38 Special revolvers were issued to police agencies in huge nembers mainly because at the time, there wasn't really anything better without going to heavy, large-framed revolvers or one of the ground-shaking magnums. Also...The service revolvers produced by Smith & Wesson and Colt were inexpensive and the companies could crank them out by the thousands. They were in big demand by police and citizens alike.
While there are more powerful choices...often read as "better"...the .38 Special is adequately effective if shot well...even in standard pressure/velocity loadings. They weren't hard to control, and the noise and flash wasn't nearly as disconcerting as the .357 Magnum. Since a large percentage of police and citizen defensive shootings occur at night, that's no small concern, and since a good portion of citizen actions happen inside the home...the .38 isn't as likely to cause your ears to bleed as the .357 is.
The .38 Special isn't as intimidating for the ladies. Not saying that the gentler sex isn't capable, but most women are put off by the noise and recoil of the mid-bore magnum, and they're not nearly as amenable to practicing with it.
Personally, I'm as confident with a Model 10 as a nightstand gun as I am with a Model 1911. In fact, a Model 10 is a permanent resident of my nightstand, with a twin on the other side for the alien creature who shares my sleeping quarters.