A little bit of clarification:
"One-Adam-12". One indicated day shift. Adam indicated the assigned police district. 12 indicated the patrol area assigned.
"Two-Adam-12" was the same basic assignment, but second shift (evening to late night).
"Three-Adam-12" was also the same basic patrol assignment for third shift (late night to early AM hours).
Radio dispatch speak, helped the dispatchers know which specific crew they were communicating with, which shift (start and end times). Other radio call signs were used to designate supervisors, detectives, special assignment units.
LA-Metro area is a massive chunk of real estate, mixed commercial and residential, broken down into specific areas served by the various police divisions, each subdivided into patrol areas with units working 24 hours per day on rotating shifts. A central call center responded to all incoming requests for services, and dispatchers assigned responding units on a "next available" basis with attention to the boundary areas and shift schedules.
The guys assigned to Shift One (probably 7AM to 3PM) in Division A ("Adam" in phonetic radio-speak), patrol area 12 (specific boundaries on a map of the metro area) might occasionally be sent to hot calls outside their basic assigned area, but would expect to be relieved just as soon as the guys responsible for that specific area were available to take over. And come "EOW" (end of watch) time they expected the next shift to take over from them so they could finish up for the day and go home.
Probably very few were as low-key and pragmatic as Officer Pete Malloy, and disputes over responsibilities and assignments were not uncommon.
I was not LAPD, but I did work on a good-sized city police department during the same time period as Adam-12 popularized. The human personality traits involved were probably similar. No one liked being sent into someone else's assigned area to take care of other peoples' problems in addition to their own responsibilities, and no one liked being held over at the end of a shift because the dispatcher couldn't keep the assignment roster straight.
Starting about 1975 or so overtime wage laws were forced on police departments, and that added some stresses to the mix. Prior to that, we might be required to work double shifts without any additional compensation (not so good for employee morale, especially on holidays and special family occasions). Getting stuck finishing up a complicated situation within your own assigned area was one thing, but spending many hours cleaning up a situation in someone else's patrol area was something else entirely.
Reminiscing about old times here. No computers. No cell phones. Many times without radio contact (certainly no portable communications for use when away from the patrol car). I remember walking a foot beat in the downtown area and relying on tower lights and call boxes for communications.
Different times.