Well, I'd rather they just get pitted. If someone is at the point of fleeing from police in a high speed chase, I want them removed from society, because nobody well adjusted and beneficial does that. Whether that's by arrest or by accidental death, I really don't mind either way. The alternative also emboldens criminals to flee as a first resort and to plan around that possibility.
Fortunately in USA we have many state jurisdictions to choose from so we can each live under the sort of laws that suit us best!
This would be precisely the divide I mentioned above. One is focused on whole-picture outcomes, the other is focused on making sure “bad guys” have a bad time (regardless of how that fits into the larger picture). Folks on either side of this divide tend to think the other is actually, factually nuts.
You are ignoring the big picture outcome of the resultant culture that develops in a society in which criminals can easily flee and not be chased. Culture shifts for the worse in an environment that is less likely to catch, arrest, or prosecute criminals. Trust and norms erode.
The factual outcomes almost don't matter; what matters is perception among the masses. For example, if people largely believe that shoplifting is not prosecuted in a city, and they see shoplifting occur, it is extremely depressing, even if they see the person arrested. It's demoralizing. It also probably leads to more attempts at shoplifting overall. I use this example because it's common enough in a few cities.
High speed chases are rare, so it's not as immediately obvious. But if people see on the news two stories, "man kills woman, cops are there, he flees in car, high speed chase, crashes into innocent bystander killing self and them" versus "man kills woman, cops are there, he flees in car, police arent allowed to chase him so he is currently at large, but they are trying to track him by other means", the latter is far more demoralizing, makes one lose faith in society and the rule of law, makes one less proud of their culture, etc etc. This is a serious effect over time.
At some level, society needs to believe that bad behaviors are punished and that good guys are trying their best to stop bad guys. This is very important to a functioning society. When people stop believing that, culture declines rapidly. Even if the utilitarian outcome is slightly better when not stopping bad guys sometimes (e.g. not prosecuting the previous president even if you could), it's usually not worth the resultant demoralization.
I broadly agree that both are important, but I think the difference lies in the level to which the person feels about the two scenarios you post. Some people are far more upset about the former than the latter (and also consider what happens if you modulate it by the crime committed).
(And of course it's not a strict either/or as well: you can have a rules of engagement for such things. e.g. in the UK the police are not blanket banned from pursuing a fleeing vehicle, but they need to have had appropriate training and do so only in particular circumstances)
