It is not as much incorrect as it is ill defined. The "quantum teleportation protocol" inherently requires the transmission of a classical bit (the weirdness is that a single bit + entanglement is sufficient to "teleport" a quantum state represented by a complex number). So, which part are you asking about when you ask whether it is "instantaneous". I feel like the need for a classical bit makes the question rather moot.
Or maybe the question is about the speed of the collapse of the entangled pair upon measurement. That question makes a bit more sense, but its answer is simply "unobservable". The observable effects are all the same independently of the answer of the question, so we do not care. The theory does not say it is instantaneous, the theory says the answer does not matter.
You can decide for yourself what this means "philosophically". For most working scientists "unobservable" means that science does not care about it, because it does not matter when considering the workings of the universe. Some of us do try to see whether some extension of the current theory would make the answer observable and also help explain other difficult ideas (but Bell inequality experiments do confirm that it simply does not matter).
Is it possible to use entanglement for communication? I could be incorrect, but I vaguely recall reading that researchers were pursuing it a while ago. Even if it's just information, being able to communicate faster than light would be neat and have some big implications. But in the article, it sounds like it's not instantaneous.. so if it's faster than light, but not instantaneous, that sounds like some kind of new speed limit?
You can use entanglement for communication, as long as you also use some classical communication channel in addition to it. If you just want to transfer bits, entanglement does not provide much more than classical communication channels (maybe a bit better signal to noise ratio when used together).
Quantum teleportation requires both entanglement and classical communication channels to be present.
And all of this has nothing to do with FTL communication. No matter what piece of known physics you use, FTL communication is simply not possible. It is not just "not known how to do it", rather it contradicts and causes unresolvable paradoxes in an enormous body of extremely well verified laws of nature.
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.
Or maybe the question is about the speed of the collapse of the entangled pair upon measurement. That question makes a bit more sense, but its answer is simply "unobservable". The observable effects are all the same independently of the answer of the question, so we do not care. The theory does not say it is instantaneous, the theory says the answer does not matter.
You can decide for yourself what this means "philosophically". For most working scientists "unobservable" means that science does not care about it, because it does not matter when considering the workings of the universe. Some of us do try to see whether some extension of the current theory would make the answer observable and also help explain other difficult ideas (but Bell inequality experiments do confirm that it simply does not matter).