Know people who use the service and like it but I refuse to. I actually enjoy going grocery shopping (two young boys in tow too). I think others have touched on the drawbacks of the service quite nicely. ie Produce and meats, basically anything that isn't processed. I'd also mention, they don't have every single product listed on their website so you may miss a few special deals in store.
I also enjoy the social aspect of seeing everyone at the store and having my boys practice at theirs.
Anyway... the service isn't for me, but I understand it is for some people.