I agree almost entirely. I'm specifically not asking for people to say "I'm a PhD in statistics, and here's the answer. Accept it because I know better than you." What I'm asking for a a complete and reasoned response, along with some evidence as to how much I should listen to you in the first place.
If you have no such evidence then the onus will be on you to make your argument more complete, more coherent, and more comprehensive. If you have evidence (note: evidence, not proof) then you can be a little less rigorous in what you say, and rely on people giving you the benefit of the doubt while they work through the argument.
What I see a lot of is long, apparently good arguments, that then turn out not to be as complete or coherent. they sometimes just don't hang together.
Significant amounts of formal study in a subject is evidence that someone might just have a better understanding. After spending a lot of time on the internet I'm tired of having to wade through every single argument in detail looking for all the possible chinks.
Maybe that's just impossible. Maybe every person has to redo every analysis for every argument. Seems like a complete waste of almost everyone's time. What about "Don't Repeat Yourself" or "Don't re-invent the wheel." I guess we are doomed to reinvent the wheel in every single discussion.