Beginning an argument for the existence of qualia with a bare assertion that they exist

But that's not contentious. Qualia are things like the appearence of tomatoes or taste of lemon. I've seen tomatoes and tasted lemons.

This is the root of all these Searle-ian arguments, and they are trivially dissolved by understanding that the special feeling people get when they think of X is also a property of how brains work.

But Searle says that feelngs, understanding, etc are properties of how the brain works. What he argues against is the claim that they are computational properties. But it is also uncontentious that physiclaism can be true and computationalism false.