That's the same excuse they used for not endorsing a GB Olympic football team. And yet they're happy for Cardiff and Swansea to play in the English leagues as you say, and also happy to use English players with non-English grandparentage, which is only so common because of the strong links between the nations of the British Isles. Surely Wales using Vinnie Jones and Sam Vokes, Scotland using Danny Fox and James Morrison and the Irish regularly using anyone with an O' or Mc in their name shows a dependance on English football which "might make FIFA consider whether they need separate representation"?
I'm sure Cardiff and Swansea are now governed by the english FA, because they felt the FAW were holding them back.