I think there's a fundamental misunderstanding that people who use a Steam Deck only ever use it in Game Mode, and that's simply untrue.

This was my claim. To put it a different way, "All people who use a Steam Deck only ever use it in Game Mode." I am a person. The parent and children from the anecdote I shared are people. We all use Desktop Mode. Therefore, it is not true that all Steam Deck owners only use it in Game Mode.

I never made any other claims. Burden of proof met.

It is not my burden of proof to demonstrate the positive claim that an "extremely small" minority is using Desktop Mode. That's your claim, and the burden is upon you to prove it.