That's not very sound. Can you name one other national team in the World Cup that can consistently field people from two countries/nation-states?
And besides rugby and cricket, could you kindly list those 'many other sports' where Ireland feld a united-island team. Let's make it semi-serious and avoid sports like curling or korfball. Big, wannabe global sports.
Footie? No.
Olympic Games? No.
Doesn't get more global than those two. Hockey maybe? Still.
We can argue whether they representing Ireland as a whole makes sense or not, but they are basically given an option that every other single country doesn't have access to.