Could know and would know are two differn't ideas.
We don't know what we don't know.
Yes, but we know what we know and we know the approximate boundaries of what we can be certain of beyond reasonable doubt. For example, it's conceivable that my house might turn transparent, or gravity will just stop working, but you need some good reason to take that seriously enough to throw out the empirical knowledge that tells us beyond reasonable doubt that such things don't and can't happen in our local spacetime environment. To claim that something unphysical, undefined, and undetectable, can have significant influence on the physical world outside of physical law is simply incoherent - a significant effect will be detectable - that's what makes it significant; physical laws describe how the world behaves - any significant influences are already included; if we haven't seen their influence, it's not significant.
If we are proposing things that are not in evidence we can't use the lack of evidence to characterize them definitively.
Meh; we've also no evidence of magic leaking through from a parallel universe, so we can't characterize it definitively... how should we treat such a suggested possibility?
Aren't there an infinite number of things we could imagine are influencing our world but are not in evidence? What should we expect if they really were influencing our world? Evidence. Have we looked? Yes. Have we found a significant anomaly? No.
If something is not in evidence when it should be in evidence (i.e. when it is supposed to have significant influence on what we can detect and measure), then we can ignore it. A strong version of Hitchen's Razor.
The problem of interaction might be a problem, but we don't know it's a problem.
Because there's no evidence for that interaction - our current models describe and predict the behaviour of our human-scale regime precisely enough that no deviations have been found within the limit of experimental error, which is well below what would be significant to our everyday lives. I submit that whether any such interaction could occur or not, it isn't a problem because it has no significant (detectable, measurable) effect.
It's an example of
Sagan's Dragon - and you can suggest that we can't dismiss the possibility of such a dragon; but when we've empirically established beyond reasonable doubt that it has no significant influence in the world, we
can dismiss it.
The model breaks down at the beginning of the universe, it is nessisarily incomplete.
What we "should" know also breaks down then.
We know it's incomplete, and we also know its bounds of applicability; but we're not at the beginning of the universe or the other situations where it's inapplicable. Similarly, Newton's Laws are incomplete/wrong, but they're reliable at everyday human velocities, and even the velocities of planetary probes. Should NASA be concerned that, after so many successful journeys, some unevidenced, uncharacterizable, non-physical influence might push their next probe off course? I don't think so.
This is part of the problem with many religious ideas, they present themselves in a way that make it impossible to evaluate them for the purpose of being impossible to evaluate.
That humans regularly propose ideas like this probably says more about humanity and their ability to honestly evaluate ideas than anything about the universe.
Agreed; but when such ideas imply significant influence on our physical world, we can investigate them, and if they're valid we should see evidence of influence that is not accounted for by our physical models. But we don't.
And then they get snippy with people who don't believe them.
That's their problem - if they ignore or dismiss the definitional problem, the interaction problem, and the evidential problem, then they can't expect to be taken seriously.