I watched a very exciting high-speed chase on YouTube about a year ago, and following that, the YouTube algorithm decided that all I ever wanted to watch was more high-speed chases. Well, I guess it wasn't wrong, I went down a serious rabbit hole for at least a few weeks... must've watched a hundred or more, before getting bored with the subject. There are entire YouTube channels devoted to high speed chases, associated with various police departments around the country.
In any case, yes... they have rules of engagement, they must call off a "pursuit" under certain circumstances. But those circumstances are not universal between departments (eg. state and local LEO's involved in the same chase), and appear to almost never actually cancel the chase. In many cases, the local will have to back off due the conditions of a chase violating their rules of engagement, but then the state or county law enforcement vehicles simply take over lead in the chase. In almost all cases, the conditions that created the violation of chase policies eventually resolve themselves, and then the local takes over again as lead, farther up the road.
The most oft-seen of these rules is when the vehicle being chased enters a restricted lane of travel heading the wrong way, such as going east in the westbound lanes of a divided boulevard. The lead vehicle will turn off their siren and fall back to follow at a safer distance, not "in pursuit" but still following, until the vehicle being chased switches back to traveling on the correct side of the median. Then the formal "pursuit" resumes. It is rare they just decide to let the perpetrator drive away, you almost never see that.
Remember, even the fastest cars on the road can't out-run police radio, and there's almost always another officer waiting farther up the highway.
The reason typically given for pursuit is indeed the danger the offender is creating for other vehicles and pedestrians on the road. If they had been operating in an unsafe manner prior to the chase, actually causing the initialization of the pursuit, it would appear difficult to make any good argument that canceling the chase will suddenly cause them to drive safely.