If not, what is the consequence?
I can think of two.
One, they become "nonfalsifiable".
Note that by definition this !="false"; it just means that in order to help avoid false positive errors, we methodologically reject such choices.
Two, they are falsifiable in principle but not in practice: which is why history is not a science, we cannot *actually* replicate everything.
But even if we accept some of these stories, the only risk is that we are incorrect. It does not mean they ALL must be incorrect.
Your error is caused by involuntarily carrying over the scientific mindset (as I said before) of "uniformity of causes in a closed system" coupled with "Occam's razor".
In science, technology, engineering, once we have a model which accounts for something, we then assume that under the same conditions, the same efficient causes are operating: so we must accept ALL stories of similar conditions (at least as "plausible") once we have accepted the putative mechanism for one.
From there it is a convenient shortcut to accept all such happenings (ECREE), forgetting that even mundane events may be factually false (shouting the N-word at Congressman Lewis) even if they are allowed by the laws of nature.
Then, carrying over this assumption to stories of the supernatural, the (mistaken) assumption is naturally made that if one ever accepts even ONE miracle, one is "honour-bound" (or at least bound by logical consistency and intellectual rigor) to accept all of them.
This then becomes an immediate reductio ad absurdum.
But the problem with this argument is, the consequent doesn't hold!.
Miracles are held to be (for the sake of this type of argument) not merely the workings of the same old uniform nature, in a way unexpected to us (cf "Cargo Cults" and their understanding of airplanes), but the explicit interference in our world, in a way, type and fashion we cannot account for.
The cynical atheists then use this as a further argument against God as unreliable or vindictive (to quote Saruman, "You may find the shadow of the wood at your own door next. It is wayward, and senseless, and has no love for men.").
But the problem is, since miracles are held to be the direct actions of a person or personages unknown by experimental methods, we cannot attribute EACH and EVERY miracle to the same source: and in fact, it is even possible, nay, preferable, to instill a lower-level ECREE to look at the source and provenance of any miracle story: men tell lies about God as much as they lie about politics. But just because people have faked miracles, or lied about them, is not sufficient grounds to categorically rule out all of them. The presence of counterfeit $50 bills does not invalidate the US Mint. (It doesn't argue *for* it either, it just argues for the presence of real $50 bills, leaving unsettled the question of *their* ultimate origin and provenance.)
Cheers!