At least in Finland, a parent can stay home and get paid something for parenting, but wouldn't it make sense to have the retired grandparents that choose to do that job instead? They could get additional income support to give them a bit more and the parents can go out and work and maybe be able to live a little bit more of life too. Of course, no one would be forcing them if they didn't want to.

They can. When my mother cared for our daughter during the day when she was 1-3 years old, we received kotihoidontuki. Were we cheating? Not really because that particular benefit is paid in order to keep a child from needing a place in a municipal daycare center. What parents pay for childcare in those facilities per month per child is very heavily subsidized. The real cost per child per month is around €1,000 whereas the means tested maximum price was something like €280 when our daughter needed full time daycare in 2014. So the idea is to pay the family about €330 per month to keep that kid from using a service subsidized to the tune of twice that amount. It explicitly says on the website of Kela that a guardian has to stay home with the child.