Same boat with my daughter. I can understand why they would want to block these features - there's a bit of a creepy vibe to the "Friends" list and the Trading feature that I'm uncomfortable with. The "Last Pokémon Caught" feature is raising my eyebrows, and the requirement to be within 100m of the Trading Partner could potentially be used to track down someone. If they aren't in range, they're more than 100m away from you, but if they are in range...
My guess is that this is a legal issue, and they either know that they can't do this for under-13's or they don't want to risk a lawsuit that they can't win (bad publicity could be worse than actually losing the lawsuit) just to allow kids to access this part of the game.