The argument is that it doesn't allow good players to get the first team experience and develop into great players.
I have never been one for advocating a quota on foreign players, but it is frankly something that perhaps should be taken seriously.
The guy in your avatar for example became great player as he was given the opportunity - as a relatively unknown youngster - to play regularly in the Premiership and Arsene Wenger made him into a world class player. Now he says - thanks very much - and fucked off. That chance could have been given to an English player to develop and who might now be playing for England.
Wenger has an eye for spotting talent. Fabregas was exceptional even when he was a kid. The reason he was given a chance in the first team before he even turned 18 was because of that very exceptional talent which, lets face it, NO English player has ever shown for many generations. He was given a chance because he that damn good.
Theo Walcott? All speed, but no real improvement in his passing, shooting, or consistency. Young English players are, lets face it, over-paid and spoiled. Their coaching as teens is not the best in the world, and even the older ones only look exceptional for teams like United, Chelsea, Liverpool, Arsenal etc because of some very exceptional foreigners in their side.
That was the reason Wenger managed to lure Cesc to Arsenal just the way Gerard Pique went to United. Pique is a brilliant defender but because of Vidic-Rio partnership he had very limited chances, but when he played he showed he was one for the future. As soon as he went back to Barcelona, Rafael Maquez was out of the first team and Puyol-Pique partner in the middle for both Barcelona and Spain.
The problem is purely and simply that English FA and most clubs often have very shit academy systems. From coaching, to grooming, to training...