Several comments in this thread give "Dropbox is just rsync" vibes. I'm curious how many of the commenters suggesting to DIY understand that having small children means essentially no free time to hack on something like that.
And it's mostly tech workers here. I would say most parents are not technically inclined. It would take the average Joe god knows how many hours to set something like this up. Even for a techie, and even if you value your time at only $10/h it would be worth it even if it took only a weekend of hacking something together, and you get something that was built specifically to your use-case.