I hate so say it but I am that guy. I have three kids and they are always going to the doctor or E.R. for something.
it stinks knowing that you are a Dilbert Employee
"Kids are the number one work avoidance device" - great, you guys: you will be the first to whine when there´s no one left but senior citizens in gated communities.
Good, reliable, organized child care and alternative "sick day" child care would be worthwhile, too. Large organizations have resources to put that together, and smaller organizations would be willing to chip in to be able to use those centers for their work force too. I don't have children, but I can see that many more people would be available to work if only they had a safe place to park their sick child.
To be frank, I have yet to see any such people who regularly take a day off for looking after their immediate family. One day sickness is the largest cause of absentism at our place, closely followed by hangovers from drinking!