In a number of European countries it's not allowed to fly on a FAA or ICAO license for that matter in a European registered aircraft. There's also the rule in some countries that a resident of that country cannot fly on a foreign license. In France a French pilot is not allowed to fly on a FAA license in an N-Reg as well.
In the US you're not allowed to fly N-Reg unless you have a FAA Pilots Certificate (full or validation)
So it would be quite easy to make it impossible for Irish citizens to fly on a foreign license without at least a validation.