But a scientific theory can have well-defined implications about unobservable things. One example is “if you send a photon past the cosmological horizon, does it suddenly cease to exist?”, which (assuming conservation of energy) would be false.
That distinction might be more subtle than you think. Just picking on your example first: The math describing that cosmological horizon is actually the same as the one describing the black hole horizon (including things like Hawking radiation). The question of what that photon does is pretty much equivalent to the question about a photon falling in a black hole. That question probably matters to a grand unified theory (and has an explicit answer in it), but at the level of sophistication of current physics, the question is mostly moot.
But notice that this particular question is something we can at least contemplate mattering. While on the other hand, we hardly can even make up an imaginary setting in which the speed of the "teleportation" matters. It is more of a sign that the mathematical treatment we are using is unnecessarily obtuse, because in a "good and proper" mathematical theory describing the effect, such "nonsensical" questions would not be able to appear.
Of course, it might turn out that the question matters in some extension of quantum mechanics that leads to a grand unified theory, but that would be a surprisingly boring outcome. It is more probable that it does not matter and we need to find a language which explicitly shows it does not matter. Kinda reminds me of this comics https://calamitiesofnature.com/post/19171164647/fairies
In this case the theory doesn't have well-defined implications. The different interpretations of quantum mechanics, which agree on the observable details, disagree on the unobservable details.
It's like an entity within a game of life simulation trying to figure out if the simulation is being run by Xlife or Golly. There's just no way to tell, and no slam dunk prior to eliminate one of them.
