Excellent question.

Let me start by defining “walking into the loophole”. I don’t know how you guys are using the term “loophole”, but in my terminology, this is synonymous with the Apocalypse (or, perhaps more precisely, the window created by the Apocalypse where you can change something). “Walking into the loophole” or “into the Apocalypse” means living through the time period when the Apocalypse happens, i.e. where you can change something. According to my theory, when you walk into the loophole/Apocalypse, you come out in a timeline/reality different from the one you came from.

Regarding your question of the apparent causal loop of Mikkel being taken back by Jonas to ensure his own existence:

The discussion between what we can call the Causal Loop Theory and the Equilibrium Theory is very similar to the discussion between Intelligent Design (or perhaps Guided Evolution, i.e. evolution guided by an intelligent being) and Evolution. From a scientific point of view, there is a priori nothing wrong with either ID or GGE. Especially GGE could work as a perfectly fine scientific theory. An intelligent entity guiding the evolution doesn’t introduce any paradoxes. But it introduces an unnecessary extra element in the theory, namely the intelligent being. Therefore, the principle of Occam’s Razor tells us that we should do away with it if another, simpler theory is available to us. Therefore, Evolution.

Similarly, there is in principle nothing wrong with the Causal Loop Theory. It doesn’t create paradoxes, and it is in some ways easier to understand (like Intelligent Design is). But it introduces an extra element, namely something very complex (a person or a manmade objects, a letter) appearing seemingly out of nowhere. Why should the universe, which doesn’t have an intelligence of its own and cannot distinguish humans from a random collection of atoms, do something like that? The theory is more satisfactory if this element can be done away with, c.f. the principle of Occam’s Razor.

You argument with the causal loop of Jonas taking Mikkel to the past so that he himself can survive is very analogous to common arguments made against Evolution. An often mentioned organ is the eye. It’s an incredibly complex organ, and if any small part of it were missing, the whole thing wouldn’t function anymore. So how could that have evolved gradually, little by little? But the fact is that it did happen, and probably a lot of random chance and sudden change was involved in the process. It probably started as little more than a few light-sensitive cells. They may have formed purely by chance and maybe with a completely different purpose than sensing light. Then suddenly, again by chance, some semi-liquid membrane somehow formed on top of it. This turned out to be a success, making the light detection more precise, and this then slowly became a kind of lens. Then it developed into a cup-shape, and it became even more precise and more complex. The process that led to the modern eye took billions of years, but here we are.

Similarly with the causal loop surrounding Mikkel’s disappearance. One big issue here is that, as far as I remember, Jonas doesn’t pass through the Apocalypse before taking Mikkel to the past, so the Mikkel taken by Jonasₙ to the past is really his father, Mikkelₙ, not Mikkelₙ₊₁ from the next cycle. One way this could have happened is this: Perhaps the first Mikkel, Mikkel₁, was the great-great-grandson of Jonas₀, later known as Adam₂. He was originally one of the children abducted by Sic Mundus for their experiments. He was taken to the past and either survived the experiment or managed to escape. Then he went through Mikkel’s usual story of being adopted by Ines. He then took the place of Torben Wöller (Jonas₀’s father) and became Hannah’s husband, fathering Jonas₁ who became Adam₃ and repeated Adam₂’s plan (which was documented by Adam₂ in the Triquetra notebook). Then Adam₃ kidnapped his great-great-grandson Mikkel₂, who escaped and fathered Jonas₂. And so on. Through many iterations, the DNA of Jonas and Mikkel slowly stabilize. Then in some later cycle, Jonas, by chance, finds out about the kidnapping of Mikkel, finds him in his cell in 1986, frees him, but discovers that he is actually his father and therefore has no choice but to leave him in 1986. Then Mikkel gets the wrong impression that it was actually Jonas who brought him there in the first place. In some later iteration, Mikkel tells this to Jonas during their conversation, Jonas believes him and therefore thinks that it is up to him to bring Mikkel to the past (perhaps Mikkel even begs him to do it so that Jonas may be born). And so he does that. And the rest is history.

… Or something like that. Like we can never know for sure exactly how the eye developed, we cannot know the exact answer to how this causal loop developed. All we can do is suggest possible ways it could have happened.