I wasn't planning on offering juice at all for the reasons above. But the poor kiddo became chronically constipated. We started offering apple or pear juice about once a day to keep a handle of things. Any time I tried to stop it (which he didn't mind), he'd be back to crying while trying to poop.
We started with juice around a year old I suppose? I wasn't thrilled, but it really helped get things sorted out.
Now we don't give it every single day, but most days he gets a cup of juice. For the same reason. I thought it was just teething related (some kids get diareha while teething...mine gets plugged up!), but doesn't seem to be since if we cut out juice for several days, we're back to our same old problem. We try to keep him well hydrated with plenty of fiber and watch the bananas and things like that they're contributing to the problem.
I don't think there's any reason to offer juice to a child under normal circumstances. Your ped should back that up...even a totally main-stream one. Usually they ask you to limit juice intake to avoid filling up on empty calories.