Oh that sounds somehow more annoying than just having to pay it yourself, seeing as you have to do the calculations yourself anyway.
To be fair it possible to be owed a refund or owe extra tax in Ireland too. If you changed jobs and didn’t inform Revenue they won’t apply tax credits until they know the full story for example. You never have to calculate how much you owe or are due though, at least not for an individual. You just tell them what your salary is, or if you’re claiming a credit.
You can do that in Ireland too. For health insurance the insurer handles the tax and takes it off what they charge you. For charities if you donate over a certain threshold the charity gets to claim back the tax you paid for themselves. For ongoing things you inform Revenue and they let your employer know to collect less tax. Then for other things you just tell Revenue and they refund you.