How did the FA let it get like this? The football league was run by the Football League, now it's run by the Premier League and the (English) Football League. The FA were never really in a position to stop it, as far as I'm aware.
I'm not convinced by the 'foreigners ruining our game' argument. We were pretty piss poor in the seventies and there were few foreigners in those days. If the FA is to blame for anything it's for not doing what it's done with the St George's Centre a long time ago. While other countries were investing in grass roots, making sure there were pitches to play on and lots of qualified coaches to teach young kids properly, the FA didn't and we've been playing catch up since.
If there is a detrimental effect from foreigners in the game it's probably more to do with foreign owners who don't give a shit about England or developing English players, backed up by the modern fan who doesn't give a shit about England, hates the international break because it interferes with club football and wouldn't put up with two years without success whilst a manager develops young players.