thank you very much for this write-up. I knew there was something off about Wii Fit when I tried it, and couldn't really dial it in until someone I know took to checking their numbers with it quite a bit too seriously.
The balance board as an input technology is quite fascinating, and it effectively gives you four reasonably accurate and high-speed low-latency pressure sensors over bluetooth. I wish the Wii would let you use the board to move the pointer onscreen, but you can do that with Dolphin now, I'm reasonably sure.
I used it for moving my mouse cursor or panning my microscope back when I had my lab, to control the other two axes in Descent and other flight simulators, or as an electronic footswitch. I was working on a homemade Taiko no Tatsujin controller, among some other projects, using $1 thrift-shop balance boards.
I wonder if it works with Steam Input on the Steam Deck? I could program up some UI overlay stuff to work with it.
Fun fact: It has a UART I/O under the battery box (which iirc carries the HID channel it uses over Bluetooth), and contains much of the requisite electronic guts of a Wii remote, including the speaker and that little memory for Mii programming.