Pardon me for using the word fate... but, IMO, ANY chase can lead to any outcome. To try and say that an officer can chase "only when" doesn't make any logical sense and doesn't guarantee that all will remain "safe"... it should be left up to the officer's descretion... period.
There is no "period" here, everything we've been talking about is a matter of opinion.
You make it sound like police officers never make bad decisions. People have been DYING because officers have been using their "descretion" to chase would-be fugitives into BUSY areas.This isn't the wild west. There are considerations to be made.