I don't think I've seen this myself, but my friend was surprised by it when she went to some extremely expensive restaurant that required reservations a month or more in advance.
I understand the reason for it, and it's not that different from seeing a menu for, say, a wedding reception or a catered business meal - those don't list prices, just options. But then again, on a limited-options menu, you don't run the risk of ordering something insanely expensive by accident.
So just for the risk of ordering something surprisingly pricy and potentially annoying the host, I wouldn't like to be in the dark about meal prices.
On the side topic of kids ordering, I think the parents would be best off providing the acceptable options to the kid(s) and make it a multiple choice selection, not an open-ended question. Acceptable could mean what they believe the kid will eat, what would be fine to share or take home if it doesn't get eaten up, and what they are willing to pay for. That's what a kids' menu usually does anyway - provide a limited range of foods with the highest probability of acceptance by kids in smaller portions for lower prices. Not all restaurants have one, not all kids (or parents) like the options on them, but I think that's the intent.