But, there isnt a pistol round alive that is more deadly than any full power rifle round at any range.
A 5.56mm isn't a "full power" rifle round to begin with. (At least, according to the NATO definition of what an "assault rifle is".) Out of an 8" barrel, you're losing a LOT. I'd rather have a 10mm out of a short barrel than a 5.56mm, since out of a 8" or so barrel, the velocity difference between the two (depending on the load) won't be that great. Even if it was, the 10mm would make a bigger hole with a lot less flash.
The military stopped using submachine guns for a variety of reasons, but it's also really easier to supply one kind of ammo and one kind of magazine to the forces.
The whole ammunition variety thing doesn't apply to the military, who are stuck with ball or AP ammo. Both of which, in either 9mm or 5.56mm, will go through quite a bit of "stuff", but on the battlefield penetrating cover is more important than fragmentation or expansion of the bullet.
Trying to hit someone at 200 yards with a 9mm is not something that would be easy to do without a lot of practice.
Not with a pistol, no. With a submachine gun I'm told it's not difficult at all. People here that have fired SMGs at range will chime in, I hope. Obviously, 9mm isn't going to have a lot left at 200 yards, though.
Submachine guns can be put into smaller packages than rifles, due to the shorter length of the cartidge. A machine pistol and a submachine gun are the same thing. MP = machine pistol.
IMI still makes the Uzi, and they sell them world-wide. The Mini-Uzi is a better seller these days. HK isn't having a hard time selling MP5s, either, and the UMP seems to be doing okay in sales. So, for better or for worse, the subgun is hanging in there.
Obviously, a large-caliber pistol is preferable to a small caliber rifle round for suppressed use, since the velocity advantage of the rifle is lost when using subsonic ammuniton. (Which bullet would you rather have at 1000 feet per second, a 77gr 5.56mm or a 147 grain 9mm?)
Rifle rounds out of super short barrels also are very loud and have very big muzzle flashes. This is bad in low light if you're trying to preserve your night vision to any extent, or indoors if you don't have ear plugs in.
However, the range and power of the intermediate cartidge rifle over the pistol cartridge subgun can't be denied. (Bear in mind that according to some FAQ page on AR-15.com, though, 5.56mm, out of a 14.5" barrel, isn't going to fragment at 200 yards anyway; the velocity is too low.)
The range can be a double-edged sword, though. Overpenetration concerns are only one part of the equation. Remember, police, typically, MISS a LOT more than they hit. The miss to hit ratio has, I've read, gone up dramatically in recent years. This is the result of inadequate training, of course, and doesn't apply to every officer out there. But, it is a general fact.
So, if you happen to miss your target, which round is going to go farther and do more damage to whatever it hits? The rifle round will. A rifle bullet at 2500-3000 feet per second is going to cover a lot more distance than a pistol bullet at 850-1400 feet per second, and this could be a liability.
As for armor penetration...well, that's a matter of ammo design. The Belgians came up with their small-caliber 5.7mm cartridge. The Russians had a better idea, I think, and simply developed a new armor penetrating 9x19mm round, that's loaded quite hot. I understand that it does just as well as 5.7mm, but makes a bigger hole when it hits.
With that, though, you're not going to get any kind of fragmentation. Fragmentation is primarily the result of a light-weight, lightly-constructed bullet moving at very high velocities, travelling through a thick medium, like a person, a tree, or several walls. The small caliber and high velocity is what allows the 5.56mm round to penetrate soft armor, and the light bullet breaks up in a thick medium. (The thick medium causing enough drag on the bullet, over time, to destablize it and cause it to tumble and/or break up.) As with range, this can also be a double edged sword; sometimes, on the battlefield, you NEED to be able to shoot through walls, trees, cars, etc., and you want the bullet to hold together and go the distance. AP ammo is best for this, but general issue ball ammo should be able to do this too, if not as well.
To wit: Both weapon systems have their place, and more than likely both will continue to see much use for years to come.