MB here. I stay home only when:
- one or both child(ren) is worryingly ill and might need to go the doctor (and I have a pretty high threshold for this)
- I am also sick
- the entire house is clearly going down w/ some sort of norovirus kind of scenario
- the nanny is sick
One of the main reasons we have a nanny is so that parents don't have to stay home for the myriad minor illnesses. Your child will get sick plenty enough for you to care for him/her! And I can pretty much guarantee that the hardest times for the child, and also the family, are the middle of the night sudden onset illnesses (usually those norovirus type things) for which you will absolutely be the frontline. Don't guilt yourself - there will be plenty of times when you'll be the only one caring for your child.

(And there may even be a time when you're all so horribly ill that you call your nanny for emergency help - as I did once!)