Speed limits fall under a category of laws where setting some behaviour by law is necessary, but equally necessary is that the law be flexible and only enforced to make sure the ‘spirit’ of the law is kept.
There is no one ‘safe’ speed limit on a road. Or rather, there is one perfectly safe limit - 0 mph. Everything else is a compromise between safety and efficiency/productivity/tolerable behaviour.
For example, when determining a public limit, you have to set it based on the least-safe vehicle and the least-safe driver, lest you wind up with a limit that is above someone’s capability to handle safely. This means the old guy in the '65 pickup with the bald bias-ply tires and slow reflexes has to be able to negotiate curves safely at the limit.
If you set the limit such, it’s obviously going to be too low for someone driving a BMW with active suspension, traction control, and with good reflexes and vision. Forcing them to adhere to the limit is not just inefficient, but impractical. They just won’t do it. There are plenty of studies which show that people tend to drive at the speed which they feel comfortable at - no slower and no faster. The trick is to find that speed on average, set the limit to that, and then look the other way as people find their own comfort zones within a reasonable band around that speed. You can’t just say there is no limit, because you need the tools to be able to bust someone driving like a lunatic. But you also can’t force everyone to exactly adhere to one speed, or you’ll get gridloc, tailgating, and eventually aggressive behaviour and aggressive passing. Clumping up cars on the road is dangerous - you wind up with tailgaters, and when people have to pass they have to pass multiple vehicles at once, which hands them out in the oncoming traffic lane for long periods of time.
Most police officers understand this - Highway 2 between Edmonton and Calgary has a posted limit of 110 km/h, but the flow of traffic on that highway is easily 125-135, depending on conditions. I’ve gone though many speed traps at those speeds with no consequences.
Police officers are taught to look not just for speeding, but for aggressive driving. It’s one thing to be going 130 in a 120 zone when you’re the only car on the road, or when there is a huge gap between you and the other cars. It’s quite another to go 130 in a 120 zone when the other traffic is doing 120 and you’re tailgating, flashing your lights to get people to move over, aggressively cutting and thrusting through traffic, etc. Police are trained to focus on that type of driver and let the other ones be, unless the speed itself is reckless (i.e. going 160).
But once in a while, a spectacular accident will happen, or a funding goal won’t be met, or tickets given won’t meet some quota, and the directive will come down from on high to ‘crack down’, and suddenly behaviour that is commonly ignored is punished. Somestimes it’s also done to ‘send a message’ when the speed of the normal flow of traffic starts creeping up to dangerous levels.
If you want to cut down on traffic accidents, the ‘big three’ things are drunk driving, reckless driving, and driving while distracted/sleepy/medicated. Speeding is a ‘contributory cause’ because when there is an accident higher speeds mean more damage. But going after speeders in general won’t do much for accident rates.