I use an older Chromebox that doesn't support Android apps every so often, and it's great for what I use it for. Google Drive, Chrome browsing and YouTube for media.
It's quick to boot to login, updates in the background with no user interference, and "just works".
As long as your kids never needed to go past using Google's office package, Youtube, Spotify, etc, then it'll be great.
The problems will start if they want to use iTunes, or run Minecraft, or whatever else kids do these days.

I've never had to touch the printing side of it, so you'll maybe run in to issues there.
Make sure to be looking for Chromebooks with 4gb, I hear tabbed browsing suffers a bit on the lower memory machines.