Overall, I think this is a pretty bad situation. It gets people used to ignoring laws, people who scrupulously follow the law are often at higher risk (and cause higher risk to those around them) than if they went along with traffic, driverless cars go awkwardly slow, some risk of selective enforcement, confusing for travelers, etc. How can we get out of this?

If we just started strictly enforcing the current limits we'd have a mess: it's too big a behavior change to push all at once so you'd see even more dangerous variance in speeds than today, and it's unclear we actually want people driving the posted speeds. It also wouldn't work well to raise the limit to the speed people are mostly going, since many people would assume they can then go an extra 5-15mph on top of that.

Instead we could take inspiration from Brazil and introduce a parallel system of maximum speeds:

Initially this has no legal effect, and just makes the existing amount of leeway more legible. On a 55mph road where people normally drive 60-65 and the police don't start ticketing until you're more than 10mph over, the signs would say both "speed limit 55" and "max 65". These would be rolled out gradually, in consultation with traffic engineers and the people responsible for enforcement.

As they roll out, you adjust enforcement to match. Put up speed cameras set to the maximum in many places, and in other places have police enforce the max strictly after each sign is put up. Traveling above the limit but below the maximum becomes effectively allowed, since there's no enforcement.

Once the rollout is complete you overhaul the laws around speeding to make the maximum the legal limit, and adjust rules that are set relative to the old limit to still make sense. For example, if you previously gave only low fines for going 58 in a 55 zone, and in practice never issued them, while you gave high fines for going 68, you would still want the higher fine for going 68 in a "max 65" zone. The goal is to bring the law in line with behavior, but otherwise keep the status quo.

At this point you could consider removing the older lower "speed limit" signs, but I think it's probably worth keeping them as advice about what speed to travel. In some cases you might raise them a bit, knowing that with the maximum in place as a firm limit you'll get slightly faster speeds but lower variance.

I think there's a path here that brings the law back in line with driver and enforcement behavior, while otherwise essentially maintaining the status quo. It does require new signs and some policy tweaks, but seems on balance pretty positive to me.