While I still lived in L.A. (80's), the policy was changed to scramble an air unit ASAP when any pursuit lasted more than a few moments. Once Air had a fix on the perp, the ground vehicles were supposed to back off far enough so he would not see them, and thus slow down. Air would then follow and bring ground back in when the perp was stationary. This appeared to work in the beginning, as back then there were usually several units upstairs at any given time.
However, in the dozens of LAPD police chases I've seen on TV and YouTube since then, it appears that, Air or not, ground units continue to dog a suspect's heels. I can only assume that the previous policy was not effectual in in the belated snaring of the bad guy.
I agree that many warrants can be served at a residence. However, you should not assume that this does not happen. My neighbor back in L.A. was picked up at his house, much to his surprise, on a misdemeanor warrant on a nice weekday afternoon by plainclothes from Devonshire Division. Every agency has different policies.
You cannot assume that the license plate on a pursued vehicle will lead you later on to his doorstep where you can comfortably hook him up. The car could be borrowed or stolen or have fictitious plates, and the registered address can be stale. For some reason, people with warrants tend to move around and not update their info. Hmm. How many of you have been pulled over, and the officer asks you if the address on your license is current? That is SOP.
As this issue is one big gray fog, I see valid points from most of the posters. The technology to shut off the ignition from satellite has been included in cars built the last few years. The technology to read a VIN "chip" on a moving vehicle with a scanner exists now. The use of these two will eventually be established.
On a lighter note:
If you have several people in the car, have them do the same thing with hands outside the doors or palms placed against the rear window. If you have a friend with a cop attitude, tell him to keep his mouth shut or you'll break his jaw.
Using the above and politeness will often go a long way towards a lesser ticket, or maybe no ticket at all. You will often be asked where you learned all that. Tell them someone that used to be in the system mentioned it, and it made good sense.