It's to do with the fact there was no Welsh League untill 1992, and also that we were effectively part of England until 1955. We have been founder members of certain leagues as the regional leagues were drawn into form the football League. We are all FAW members, and even now if we have a disciplinary issue there is some sort of representation from either the PL/FA/FAW in some sort of bizzar set up to administer things. As a Swansea supporter I believe that we should be a FA member not a FAW one. The FAW have a strong Cardiff bias and their decision making has been extreamly dubious, red cards being overturned that were there was no clear or justified reason to do so. Usually, no always when it was a Cardiff player who comitted the offence. The one that springs to mind was the Purse one that got overturned because he would miss the FA cup final. Enough on that tho.
There is still an issue however with us and being eligible to play in Europe under the current set up. However thats something that isn't important at this moment.
As for Rangers/Celtic/Any other Scottish club playing in the pyramid, yeah it's a question of where they enter most of the people I have heard think its a god given right that they should go straight in at the top, or at worst the championship. Not sure if you wouldn't be welcome and if the logistic thing would be an issue. Swansea to Newcastle is about the same as Swansea to Glasgow.