Police training isn't anything like military training. Lower physical standards. Police enforce law, the military kills the enemy, and police are always in control of their surroundings. Military units function in enviroments where they oftentimes don't (comparing units like SWAT to special ops groups like Navy Seals). Swat can shut down and evacuate an area in their city and focus on taking out or negotiating an enemy to surrender. Military has to fight in an entirely unique and hostile enviroment where EVERYONE might be an enemy or it might be wired to a hugeass IED.
You'd have a hard time comparing military combat MP's to everyday police.
Only upper echelon police forces get any sort of military training. And we aren't talking about SWAT. Things like the FBI's Hostage Rescue Team, the US Border Patrol's Bortac, some specialized police forces of the CIA etc.