Not any more, though, with the latest update to the Wii, the SD Card Menu brings with it the ability to play games stored on, you guessed it, an SD card. Yes, the annoying shuffling of games is no longer required. Although game save files do need to be on the Wii, still.
The SD Card Menu provides 20 pages of 12 games, or 240 total possible titles which should be more than enough for all but the most avid of downloaders. Especially with the Wii supporting up to 32GB capacity cards. Games can be saved directly to SD card once purchased, too.