If you Google "Wii U slow WIFI" there is a lot of info. I have a lot of experience in setting up networks, and after trying all of the suggested fixes posted on the net, I'm convinced that the speed limitation is caused by the Wii U.
Where are you going to see bandwidth utilization on the Wii U wireless adapter? Or are you referring to the bandwidth past the router? If that is the case you can create port forwarding rules, turn on UPnP, and set up QoS on your gateway to ensure better bandwidth allocation to the Wii U. Also, if you are looking at bandwidth utilization during a patch or game download, it probably has something to do with your distance from the ISP hub, and the connection with the Nintendo servers, which really can't be helped too much. If you are looking at bandwidth utilization while idle or simple web browsing, it would have no reason to ramp up utilization. Your connection to the wireless gateway should be 54Mbps+ depending on whether or not it is an N device.
I haven't tried speedtest on the Wii U yet because I have been rather pleased with the network speeds thus far and didn't see a need, but I might try it just to find out. It isn't like Nintendo is forcing a proxy connection on the device, but it is constantly connecting to MiiVerse. If the bandwidth between the Wii U and a remote server is being limited, I doubt very much it is anything other than the way your network is set up.