The opposite effect would be too weaken the England team, wouldn't it? Has that happened?
It's up to the clubs to handle the fee and wages side of things, I suspect the FA don't care about that consequence.
It takes time for this stuff to work its way through, however you are right that too many English players take the big coin to move to a big club, then find themselves way behind more talented foreign players.
In the end those players need to figure that out, and not being called up for England might help them.
Obviously the next player at risk of doing that is Sterling, should be find himself sitting on the bench at City, he might find his England career stalls too.
In a few years we'll know if it has increased the number of minutes played by home grown players, which is supposed to be the first step in this process. Also we should see more youth team products getting chances across all the top clubs, as despite too many having seemingly bottomless pockets, they'd all rather have a player for free than buy one.