Dragnet was first filmed in the late 1950s and then was revived into the 1970s.
Adam 12 was filmed in the late 1960s and up to around 1975.
Sometime in the middle to late 1970s there was a very good article in Guns and Ammo about the history and current status of firearms in the LAPD. I think I still have it, but I'll be damned if I know where it is in my house.
This (also from G&A) article from a few years ago talks about firearms from 1984 on, and sort of surveys revolvers, but it appears to be strictly from the perspective of a uniformed officer.
The only possible reason I can think of as to why LAPD might have required everyone to carry the long-barreled revolvers is because of the increase in violent drug crime in the 1960s. The 158-gr. LRN bullet was still standard issue into the 1970s, so it might have been a somewhat desperate attempt to increase stopping power without changing ammo or going to a more powerful gun/cartridge combination.