It isn't limited to whitewalls specifically-- tire styles are passing fads like any other. When specific tires start falling out of favor with consumers, any vehicle still rocking (new) ones of the deprecated type was presumed to be part of a fleet or motor pool. Fleet procurement tends not to concern itself with staying trendy.
Police spycraft has advanced since the 60s though so to avoid these issues they borrow from the pre-auction pool.
https://goo.gl/images/fpH49i
It isn't limited to whitewalls specifically-- tire styles are passing fads like any other. When specific tires start falling out of favor with consumers, any vehicle still rocking (new) ones of the deprecated type was presumed to be part of a fleet or motor pool. Fleet procurement tends not to concern itself with staying trendy.
Police spycraft has advanced since the 60s though so to avoid these issues they borrow from the pre-auction pool.