Well, the subject of "arguments" for or against the existence of God was first brought up in this thread by ibidem, I believe. I entirely agree that verbal reasoning is not the only or even the main sort of evidence we should examine in this matter, unless you count as "arguments" things like verbal reports or summaries of various other sorts of evidence. It's just that verbal "arguments" are how we communicate our reasons for belief to each other in venues like Less Wrong.

That having been said, it's not clear to me what you think the alternative is to saying that beliefs need to be supported by "evidence". Saying beliefs... don't need to be supported by evidence? But that's... well, false. Of course we do need to make it clear that "evidence" encompasses more than "clever verbal proofs".

Personal experience of supernatural things does tend to be statistical flukes and/or hallucinations, so dismissing it as such seems reasonable as a general policy. Extraordinary claims require etc. If someone's reason for believing in a god entirely boils down to "God appeared to me, told me that he exists, and did some personal miracles for me which I can't demonstrate or verify for you", then they do not, in fact, have a very good reason for holding that belief.