Are they? Scientists are utilitarians. If they don't have a good answer for a problem they assume it's not a problem. (I get the argument that's made. If you waited for perfection you'd wait forever. But it's a fundamentally philosophical position. You should be allowed to disagree. For example, you could choose to wait for ever. Hell, you could choose to be wrong, and as philosophy goes, that's certainly a valid position. There's people arguing that an example of choosing to be wrong is morality, and it's a pretty good argument)

For example, what does every theoretical statistics textbook say about both kinds of out-of-distribution predictions? (statistics can only predict continuous functions in the ranges it has data about. And this is badly expressed. In reality there is a "minimum smoothness" the function must have if you want to be successful in predicting (ie. no spikes), and the smoothness requirement gets relaxed somewhat if you have more data, but not much, even with extreme amounts of data. Out of distribution predictions, of course, lead to disaster regardless of how much data you have, as the data is irrelevant).

I get it, "theoretical statistics" is a synonym for "nobody has ever read it, nor ever will", but it kind of is what the whole thing is based on nevertheless.

No worries, I'm sure machine learning will solve it all, of course.

Not that the IPCC report uses theoretical statistics. I would call what it uses "political" statistics. Not in the sense that they choose the outcome (perse), but in the sense that they use methods selected to maximize participation (e.g. giving absolute maximum credit). For example, how do you average 20 models, all based on different principles? When you don't know which is right? Well, it's easy, really. You take out 2-3 models you don't like (but still mention and credit them), then average the models' predictions. And that theoretical statisticians say "that's unfair! Here's a proof can get any prediction you want that way!" is met with "shut up" comments. Well, after checking if that proof wasn't wrong, of course. It wasn't.