there are a number of reasons first is often training. Many police officers in the US have served in the US military as such they have a high degree of hands on with the AR15 series. But there are other carbines used by some Police departments in the US. Second is as you pointed out. But not all get surplus carbines from the DOD the prices of carbines to SMG because of the market are about equal to beter favoring AR. But not just the carbines themselves but the accessory market. Take a MP5 magazine for example. The MP5 is normally the chosen SMG for law enforcement. The magazine costs about $80.00 commercial just for an empty magazine. With the exception of the KRISS SMG, most SMG use proprietary magazines where as 5.56mm carbines tend to use a standardized magazine that is commonly offered on the market with lots of makers building to or better then spec. The best on the market the Magpul Pmag between $15 and $20 commercial.
Logistics and Budget. If you are a smaller police department and need to stock replacement be magazines for your long guns a hundred $80.00 magazines is probably going to be a hard expence to justify.
okay this is going to take a few to deal with. First and foremost Police and law enforcement are not limited by treaty like military. Actually technically the convention only bars use of a weapon by a signetory. Some nations could by not being signetors use whatever they want. But that's an aside.
First, military counter terror units like SAS and Delta force who have designed aircraft hostage rescue operations, don't worry about 5.56x45 vs 9x19mm because they like law enforcement in general are allowed to use rounds other than the full metal jacket. Hollow points and frangable rounds are designed for be leathal but not barrier penitrating. They would do damage to a human or animal but not perce the skin of a Aluminum aircraft.
Infact a common complaint about 556 has been it not penitrating barriers like wood vs 7.62x39. Many police departments have been more worried about 9mm over penitrating.
One of the biggest reasons why for the US that the 9mm fell from favor of long guns was the north Hollywood shootout. Where in two terrorists/Bank robbers loaded to the teeth with illeagally modified weapons be and homemade body armor robbed a bank and set to turning part of Hollywood into a warzone.
In there rampage they used 7.62x54mm, 7.62x39mm,5.56x45mm and 9x19mm they chose and used ammo optimized to penitrate barriers and built armor resistance to the standard pistol rounds. The LAPD one of the arguably best equipped be police agencies in the US was forced to run to gun stores, borrow long rifles and ammo to match these guys.
After that point the writing was more or less on the wall. SMGs were invented in the first world war because troops needed a weapon as mobile as a pistol with the fire power of a Machine gun to sweep trenches in close Quarters.
The assault rifle carbines was the product of taking that lesson farther and creating a weapon as mobile as a SMG with the range of a rifle and the rate of fire as a machine gun. With personal body armor able to be made by two terrorists ( they may not have been AQ or Islamic but they wanted to cause terror) in there garage the SMG as a means to trying to stop a dedicated assailant intending to create mass casualtys was over.
Well, firstly, the armoured bad guys example you gave was an anomaly, not the norm. If we just look at the statistics by number of attacks and casualties caused world wide, you could just as easily (if not more so!) argue that cops need 50 cal anti material rifles to better deal with terrorist vehicle ramming attacks. 50 cal also defeats body armour.
You are trying to have your cake and eat it too by arguing cops can use non-FMJ rounds, on the one hand and yet on the other also cite the (very arguably) better anti armour properties of 556 against 9mm when dealing with the as yet, extremely rare, body armoured shooter.
If the cops are loading hollow points, those rounds are not going to be any better against body armour, even just basic Kevlar, compared to 9mm.
Conversly, loading AP rounds to deal with body armour makes over penetration even more likely to the point of inevitable.
When it comes to ammo, the same market forces you mentioned on magazines also applies.
For 556, hollow point ammo is many times more expensive than FMJ because very few buyers want 556 hollow points.
Magazines are semi fixed costs in that you only need to buy more very rarely, but ammo is very much a variable cost, and police departments go through huge quantities very regularly from training alone. So even a small price difference will add up quickly.
Those UK cops I mentioned earlier were carrying see through mags, and they were loaded with FMJ, and I would bet most US police departments only stock FMJ on cost grounds for their 556 also.
For 9mm, hollow points are far more common, so the price difference is much smaller.
On your second point, the better armour penetration potential of 556 against 9mm really is only academic, because any bog standard ballistic plate people can buy off the internet for a hundred dollars are rated to easily stop 556.
Indeed, in the last instance where an attacker wore body armour in Baton Rouge, the police were armed with 556 but that didn’t seem to help them much in taking him down with firearms did it?
Against anything other than pure Kevlar vests, 556 has no practical advantage against 9mm when it comes to armoured assailants.
If a terrorist or criminal is going to the trouble to armour up, they are no going to stop at Kevlar only.
In America, it’s a different world because of the military grade weapons and armour that civilians could buy without restrictions or questions in most places. So the shift in police going for military grade weapons is more justifiable and understandable, though still regrettable. But for the rest of the world, where there is no such issue, using military rifles and ammo for everyday police action is questionable at best, and irresponsibly dangerous at worst in by book.