Indeed, people who make no claims have no obligation to prove anything, but we still do have natural explanations for things. We do have evidence for our natural explanations. We can bear that burden, even if we have no obligation to do so. And people are much more likely to walk away from superstitious explanations if they have an alternative explanation to fall back on.

Sometimes I fear in our exuberance to clarify how burden of proof works, we neglect to share alternate explanations for things, and theists imagine we don't have any. Maybe sometimes, just for exercise sake, we could step up and pretend for a moment our opponents actually want to learn something. I know we'll almost always be disappointed, but it's not like asking them to bear a burden we all know they cannot shoulder is causing them to engage in deep reflection and exclaim, "Gosh, I am struggling to bear this burden! Maybe I should consider that my cherished beliefs are founded on confirmation bias and baseless traditions, and go pursue an education on my own!"