GoFullAuto nailed it squarely on the head. Probably because he's there and lives it daily. Excellent post, thank you!
Lots of folks said "because its cheap". That's incorrect. You've got it backwards. Everybody doesn't use it because its cheap, it's cheap because everybody uses it. 40 years ago, when I began my serious interest in guns and everything that goes with them, the 9mm Luger wasn't cheap. Often it was slightly more expensive than .38Spl or .45acp, on local shelves. It was not a bargain round. Today it is, because of the volume of sales.
Likewise the idea that American cops need big guns because of how fat we are, as a people, is another red herring. It sounds reasonable, but is far from reality.
Look at US history for a while and you will see that some police agencies went to the 9mm before the US military adopted it, but not many. And many did not go to the 9mm for years after it became our service round. It has been discussed in detail before in other threads (so search), but the basic reasons the autopistol and the 9mm round took over the US police market were (not in order of importance) prestige - when the FBI adopted it, so did a lot of others, a shift in emphasis in attitudes -the war on drugs, militarization of the police, greater concern for officer safety (so police could now use hollowpoints), and mainly cost. But not the cost of the guns and ammo in 9mm, but the cost to police agencies of the purchase. Changes to seizure laws meant that police could spend seized drug money on guns/ammo, so for the depts, switching over to 9mm autos, they were nearly free. Add in slick aggressive marketing by several gunmakers, and the 9mm becomes the dominant US police round in a few short years. And as a result of that, becomes hugely popular in the private sector as well.
As already noted, European police are armed by the central govt. Individual depts don't have the luxury of / have to shoulder the burden of buying their own guns. The choice is made by politicians, advised by the "experts", and everybody gets the same stuff.
Mentioned was the 72 Olympics and the change in attitudes concurrent with the rise of terrorism in Europe afterwards. The officials decided that the 9mm was needed for police (among other things) and so that's what the police got.
A big part of the equation probably has to do with the fact that, so far as I know, no European law enforcement agency has ever tried to trot out weapon caliber as a convenient scapegoat to cover up systemic flaws in how they do business, officer errors on the ground, and a chain of command that was negligent in letting guys go cowboying off to their deaths, a la the FBI and their Miami debacle.
Now here is another factor, political (meaning bureaucratic) opinions. The Miami fiasco generated
political conclusions that led to the move
away from the 9mm round. Our "best and brightest" agents
couldn't have screwed the pooch so badly, something else must have been at fault, and the blame landed on the 9mm. This eventually led to the .40 S&W. Note that while searching for a replacement for the 9mm, the FBI authorised its agents to (go back to) use the .357mag (.38SPL+P) and the .45ACP!
In Europe, there was no such decision as a result of any percieved "failures" of 9mms.
The real question is why is the 40S&W caliber a popular choice for our LEO agencies?
Short answer for this one, it splits the difference in size between 9mm and .45, so the bigger bullet appeals to the large bore faction, it works in 9mm frame size guns, appealing to the magazine capacity faction, and it works tolerably well, appealing to the on the street faction. And, mostly, its not the 9mm (which the FBI said failed) and it isn't the .45 (which is too old fashioned). We have a cultural bias towards the newest, latest and greatest, so we are constantly re-inventing the wheel. And, since the new wheels do roll aceptably well, we are happy.
The 9mm has been, and will continue to be the European round of choice for combat. Its our choice now too. It is an efficient and effective round today (which, in the US wasn't always the case) and has become the world standard everywhere, excepting only those former ComBloc nations still using their own standards.