The Mrs. handled all the insurance for our spawn, though I myself have a VHIS policy despite "private hospitals sending you to public hospitals" - because at the end of the day it depends on the illness.
My Mother got excellent care through the public system. It wasn't a saveable ailment unfortunately, but so aggressive and urgent it was that public hospitals handled it immediately and ironically with the same top surgeon that one could otherwise pay six digits to book in the private system.
Where the private sector would be useful is e.g. if you need a gallbladder removed and the public system will stick you on a waiting list. I presume these comparisons are equally valid for children.
Stick the money in a fund instead? Sure... it may grow beyond what insurance will repay you. The fundamental rule with insurance is it's not a money making scheme and shouldn't be compared as such. You might get your money back at best, adjusted for inflation.
But stick the money in a fund then get ill six months later and you won't have made much to cover medical costs. Insurance will give you that coverage from Day 1 (or 30 to be pedantic).
Wife / child policies are through CTFLife. Comparing to mine at AXA it does seem a better deal (fewer overheads without the global branding glutton?). Her broker is not the most efficient but is an honest bloke who doesn't try to oversell. Happy to pass on a recommendation if ever an additional one is needed.