That is a box which you should not box yourself in because there are things which an intelligent mind is certain of even if you cannot produce empirical evidence to support them.
What you're saying is that if I insist on evidence for things before I believe in them, I'm closing my mind off to things that are true but for which there is no evidence.
And that may very well be the case. But what
else am I closing my mind to? I'm closing my mind to all the things for which there is no evidence because they're
false; that is, by insisting on a rigorous standard of evidence - which around here just means "any" - I'm closing myself off to a lot of lies, misrepresentations, fabrications, nonsense, and other things that corrupt and dilute the power of reason.
So, on balance, I think it's a net good to close yourself off from propositions for which there is no evidence. As they say it's good to have an open mind, but not so open that your brains fall out. Going around believing any old thing at all just leads you to confusion, poor knowledge, and a general paralysis of reason because
you can't know how anything actually works.