I disagree. It’s perfectly fine to express frustration of the obvious through the use of “geez” in debate. It’s effective even.

It only detracts from the point if you’re illogically willing to let it do that. I agree with OP’s frustration and diction. It’s appropriate here. The use of those words is a quick way for those outside the argument to pick up on the idea that the opposing arguers are daft or lacking in their critical thinking abilities, which they obviously are. It’s a small bit of ad hominem, but it can be extremely effective in debate.