No way, cops can abide by the laws citizens lay out democratically. QI was basically magic'd out of the judiciary's dignified asshole with no basis at all in legislation. It's extra-legal thuggery.
People don't get immunity for regular jobs. Just don't do crimes. IMO they should lose all immunity the moment they exceed their lawful authority. I would, in particular, have Cheney tried and then strung up from a dead tree.
This highlights your ignorance as to what Qualified Immunity is [1][2], which is different than Sovereign immunity, or Statutory Immunity.
Government Officials would still enjoy differing levels of immunity in the course of their official duties, however qualified immunity specifically is a court created immunity that is a scourge upon the legal system that should be done away with. The legal system has methods to shield government officials from liability for doing their actual jobs, while not allowing immunity for abuse. Qualified Immunity simply shields government officials from liability for abuse