How do you know the other FAs weren't approached? If they weren't, how did they get the chance to refuse?
They approached the English FA because the other nations made it quite clear, LONG before the Olympics, that they wanted nothing to do with it. Only the English FA were interested, for the first time ever.
And the separate home nations can't play in the Olympics as separate countries, because, for the sake of the Olympics, they aren't.
As to the individual players from Scotland, Wales and N Ireland, it was made quite clear that the various FAs had no right to stop them from competing, they did this with threats and intimidation, nothing to be proud of!