There's a few reasons to have health insurance for children, even though there are no private hospitals for children.
Firstly, if you don't have a medical card or health insurance for a child, if they are admitted to a public hospital for a stay or day case procedure
there is an 80 euro per night charge upto a max of 10 nights per year. 80 x 10 = 800. This nightly charge also applies to adults in public hospitals.
Secondly, as Monbretia mentioned, it gives the option to go the private route within the public childrens hospitals.
Lastly, for children aged 3 years +, the 3 hi-tech hospitals in Dublin, (Blackrock Clinic, Mater Private and Beacon) and some other private hospitals offer a range of paediatric surgery and procedures which is another alternative option if waiting lists are too long.
So its more valuable than you may realise and worth having, just in case.
Snowyb