It appears, particularly from the initial responses, that many have misunderstood my question. I am not asking why police do not open up, guns blazing with all available firepower, any time the believe the possibility exists they might be able to hit the radiator of a fleeing vehicle. I had thought I was clear on that, but apparently not.
What I am asking is why they never employ a strategy of using a sharpshooter with an accurate, small caliber weapon to disable the cooling system of a fleeing vehicle. Do a google search on lengthy police chases where they chase the fleeing vehicle for dozens of miles, down limited access highways. The police often will close the entrance ramps in advance of the fleeing vehicle. I listed two such occurrences in my OP, there are many others.
The use of spike strips is fairly routine these days, and if they have the time to set up a spike strip deployment, they could probably get a sharpshooter in place. If done intelligently, the vehicle operator probably wouldn’t even know what was going on, at least until the “check engine light” came on, and even then, he’d probably just ignore it. Those in pursuit, however, would know immediately if the hit was successful as the smell of anti-freeze is quite distinct and unmistakable.
And, yes, it just is true that an ICE will be severely disabled in a matter of minutes if it looses coolant. A modern one would probably simply shut the engine off when the temperature got too high, while an older one would last until it blew a head gasket. When that happens, it might still run, but not in any big hurry and not for very much longer. Yes, the Navistar engines a while back were capable of running about 50 miles or so with no coolant, but they wouldn’t go much longer without shutting down, and during that time, they did not make much power.