That's the problem right there, its not just an Irish passport, its an EU passport. Lets say your child is working in Germany and the EU passes a law stating that all EU citizens living in the EU are liable for conscription regardless of the EU state they reside. Your child is living in the US and there is a major economic hissy fit between them and the EU and they demand all EU citizen leave the US. Your child is an EU citizen and claiming to be British will not carry much weight if on an EU passport you are traveling and living. Its an odd world we live in and you never know what the future holds.
That's getting a bit convoluted... I doubt EU conscription is going to be introduced overnight etc.. but they do have the option to renounce citizenship if they have UK citizenship and/or indeed make sure their US visa is via their UK passport. I think in general dual nationality is more useful to have than not... not that I'm denying there could be issues... you're right to raise them but I suspect that most could be avoided/mitigated too.