That's not the reason for it. Rather, there's a very high premium put on having third-level education in Ireland as it was historically one of the ways to get out of poverty, even if that meant emigrating elsewhere. We could do with more people actually doing vocational courses on the German model, but owing to shifts in our economy, that's not as popular as it once was.
Also, education in Ireland isn't quite free. Sure, it's inexpensive compared to, say, the US, but the important thing is that access to third-level institutions is radically egalitarian, practically to a fault, owing to how entrance into third-level education works, based on a points score from your top six subjects in your final second-level exams.