That's how it works. The Wii's main controller is the Wii Remote. Any extra controllers that are NOT a Gamecube Controller should be plugged into the socket. If you don't want to get a Wii Remote +, which is needed for Wii U games that support it, you can get an original one for cheap, maybe less than $20. To play Xenoblade Chronicles or any non Wii-Remote game that does not use a GameCube Controller, you must buy a Classic Controller or a Classic Controller Pro. There's not other way around it.
You can't use a Wii U gamepad for Wii games because it is not backwards compatible that way. If you want to play Wii games on the Wii U, you must use a television as usual.
Braving the pillow gauntlet.