Ome of dad’s friends was a CHP pilot. He was based at the Barstow-Daggett Airport (dad was a Flight Service Specialist there) and flew a Cessna 180. Having conventional gear (with large mains) gave the 180 the ability to land in the desert if needed. (And I remember CHP Bob having done that at least once, though I don’t remember the circumstances.)
Anyway, Cessnas. The popular 172 (which I’ve always thought of as a tricycle-gear version of the conventionally-geared 170) first flew in November, 1955. In 1960 the straight tail was replaced by a swept tail (172A) and shorter landing gear (172B). The 172D got a wrap-around rear window in 1963, the 172F got electric flaps, the 172G got a pointier spinner in 1966, and the 172H was the last of the Continental-powered 172s. (Dad’s was a 1970 172K Skyhawk, which was Lycoming powered.) I think it was 1972 when the 172 got a longer vertical stabiliser extension and tubular landing gear struts replaced the spring steel of earlier models, which also changed the aircraft’s stance on the ground. (I’ve always thought the earlier 172s looked more ‘jaunty’.) IIRC the flaps were limited to 30°, down from 40°, at this time. Production continued until mounting insurance costs caused by ridiculous awards in lawsuits caused Cessna to stop building single-piston-engine aircraft in the early-'80s, and resumed once Congress passed the General Aviation Revitalisation Act in 1994.
But here’s the thing: Unlike a car that has been in production for half a century, the 172 still has the same basic structure. The differences are more or less in the details. Paint a 30-year-old Cessna in the current scheme, and I don’t think I’d be able to tell the difference between it and a new one from 50 feet away. So ‘primitive’ is probably not the right word to describe GA aircraft. The improvements have been incremental and include such things as improved engines (which themselves share the same basic layout as they did in the 1930s), improved avionics, and improved sound insulation.
Similar observations can be made about Piper, Beechcraft, and other aircraft. Why do the manufacturers keep making ‘50-year-old airplanes’? Part of it is ‘If it ain’t broke, don’t fix it.’ There’s little reason to change something that works. Another reason is the fear of lawsuits. We live in a litigious society, and lawsuits brought GA to its knees in the early-‘80s. Even if a change has nothing to do with a crash, someone will sue based on there having been a change. And the plaintiffs’ lawyers try to weed out anyone who knows anything about aviation during voir dire.
Does it make financial sense to use aircraft? In 1976 by dad bought his 1970 Skyhawk for $10,200. Today a six-year-old Skyhawk will set you back close to $100,000. A new one is closing in on $200,000. (Last time I checked, which is a few years ago, they were $175,000.) A 1970 aircraft will fetch around $40,000 nowadays. There are so many aircraft in police use throughout the country, that I can’t say what everyone uses. 172s have a maximum speed of about 135 mph, which is fast enough for most speeders. 182 Skylanes are faster and are better in mountainous areas due to their better climb performance.
Depending on the purchase price (there’s really no reason not to use an older aircraft) it’s not all that expensive to buy a patrol aircraft. They can cover a much wider area than a ground vehicle, and can take a straight line to where they’re needed instead of having to stick to the roads. A 172 will burn about 9 gallons/hour. Lycoming engines have a TBO (Time Between Overhaul) of 2,000 hours, so a busy flight operation that flies 8 hours per day per aircraft would need to rebuild the engines once a year. I haven’t checked the cost of that, but I’m guessing a rebuilt engine costs around $25,000 or $30,000. Then there are the 100-hour checks, annual inspections, oil, repairs, etc.
A patrol aircraft generates revenue by catching speeders. If an aircraft can replace a couple of patrol cars, then perhaps it is cost-effective. But another advantage of an aircraft is that it can be over an accident scene before a patrol car can. Not everyone drives on freeways all the time. On a little-travelled road a patrol car may never know there has been an accident, and passers-by may be few and far between. Discovering an injury crash a half-hour or an hour sooner than someone else might save a life. Another reason for aircraft is that they are useful in crime investigations. Consider a meth-lab out in the middle of a desert. A patrol car would be a give-away. People tend to notice helicopters flying around. But who pays attention to the dowdy Cessna? If the meth-maker notices it at all he might think it’s just someone out poking holes in the sky.
As for why a ‘primitive’ aircraft may be chosen for patrol work, older models are, as I have said, relatively inexpensive. (For businesses and government agencies. Not for me! 
) Certainly they are much less expensive than a helicopter, both in initial purchase price and in ongoing maintenance. And, in the case of Cessnas, which I think are the most popular choice, they have high-mounted wings that make it easy to look down at the ground. (Maules are another popular choice. They have high wings, and most of them also have conventional gear and STOL capabilities.) They fly slowly and can orbit a stopped vehicle closely, pace a car that is doing the speed limit or is speeding at the speeds most people speed, and can keep up with many or most cars that are being driven flat-out. Their altitudes can give an observer with a pair of binoculars a much wider field of view than is available to a ground-based unit.
