Redundant “necessarily”?

Let's take the sentence at face value and analyse it. To make its logical structure clearer, let's use P to stand for our prediction of the pandemic. Given that could expresses possibility, the sentence says:

It was not possible that P was necessary.

As necessity and possibility are interdefinable, this is logically equivalent to:

It was necessary that P was not necessary.

Is that what was intended? Almost certainly not: outside some highly specialised contexts, people very rarely think or speak of nested necessities/possibilites. The original use of necessarily is thus not meaningless, but, taken at face value, gives the sentence a mind-boggling meaning that is far from what was probably intended. The obvious solution is not to take necessarily in the original formulation at face value. In fact, one is most likely to get the intended meaning if one simply ignores its presence.

I just heard this on BBC Radio 4: “We could not necessarily have predicted the pandemic”. Am I right in thinking that “necessarily” is meaningless in this context?

No, I don’t think “necessarily” is meaningless. It changes the likelihood the speaker imputes to the question whether the pandemic was predictable.

The world had two 21st century coronavirus events: SARS-COV1 and MERS. Some coronaviruses also circulate among humans as one cause of the common cold. That a novel coronavirus could become pandemic was a possibility, not necessarily predictable but not beyond imagination.

With the mere snippet, it is not possible to know what the writer intended. But necessarily is suggestive of possibility.

Here’s a snippet from Ngram:

Bryan J. Rooney, ‎Annabel Ness Evans · 2018 · ‎Preview · ‎More editions A statistically significant effect is not necessarily important and may not be worth the attention of researchers.

Clearly necessarily is essential to the sentence.

No, in this context, necessarily is a hedging term; it isn't meaningless or redundant.

If you remove the term you get this:

• We could not [ ] have predicted the pandemic

This states that prediction was impossible.

Substantiating this requires showing that not only was it the case that no one predicted it, but also that no one was able to predict it.

You could refute this modified statement by postulating a set of research labs that had been battling with similar strains in years past. Clearly, prediction was not impossible. You could also point to actual predictions such as the following, which was quoted by DH Web Desk, citing Brown's book "End of Days":

In around 2020 a severe pneumonia-like illness will spread throughout the globe, attacking the lungs and the bronchial tubes and resisting all known treatments.

With necessarily in your quote, the author is not stating that prediction was impossible. The claim is instead that the certainty of such a prediction was impossible. To use the phrasing suggested by Lexico, the claim is that prediction was not inevitable.

Substantiating this (original) version requires just one person who didn't predict the pandemic. Conversely, to refute it, you would need to show that every person would have predicted the pandemic.

The original version (with 'necessarily') has a burden of proof that is so light as to be trivial, whereas deleting 'necessarily' makes the burden of proof so onerous as to be (almost?) impossible.