Knowing a couple of police pursuit drivers, the main reason to back off from a "chase" is actually public safety, and not the safety or well being of the suspect being chased. By backing off and keeping distance, the suspect usually slows down a bit and takes less chances, meaning there's a reduced chance of a member of the public being killed or injured.

The back off is not in every case either, just ones that represent significant, or increased danger to either the public, the officers, and yes, also the suspects.

Also, the Americans don't go on "ends of the earth" chases. They only chase to the borders of their jurisdiction, and when reached, the chase is turned over to the officers of that state/county to continue if need be. Also, they also back off if needed to "calm" a chase if significant or increased danger is posed to the public/other motorists.