I was referring to TonyD's point (#1649) about Wales "wanting to keep its NT" - only UEFA could withdraw recognition for whatever reason (not that they're going to do so over this matter).
As for the rest - you're quite correct. I dare say the FAW would like to have the big clubs involved in the League Cup, but it may be that the other Cymru League clubs could object, since it would invariably mean one European place fewer for one of them.