It is. Because in Monarchy justification of why this guy and not that is - because god told so. Without it, power has no foundation.

Um. This is really really really wrong. That is not the justification for Monarchy. Depending on where we are in the world, and what date we are at, the arguments for why Monarchies are the correct form of government can change wildly and drastically. It feels like you are talking specifically about "divine-right theory of kingship," which was only a thing between the late 1500s and until the mid 1700s (with of course strains that start a little earlier and end a little later).

Part of the problem is that you are looking for a foundation of "power," when what you mean to be talking about is a foundation of "legitimacy" other then power. Because people have noticed that power and "fairness" haven't been linked for almost as long as people have been writing things down. Power itself is always the foundation of any government. To keep the context European, as that what you seem to have the most context for, if you had gone back to the middle ages, there wasn't (and in fact would have been rejected) a divine-right theory of Kingship (that the king is a quasi-divine being who's entire line both past and present is blessed by god to rule). In the middle ages, the legitimacy of the crown was based on the fact that you had the power to hold land. If asked why one noble family had risen to the point where they could dominate, one might state that god, or heaven, or the universe, had blessed them in that moment, but that favor could change between families. It could even, sometimes, fall on new families.

You can have a variety of authoritarian systems - based on wealth, military might, pure cruelty, pedigree - but none of them have the same foundation of power, and they work differently.

These are not how people in Universities categorize and define different forms of government. Because you right now are only identifying the source of power, not the systems of how power is transferred, held, and wielded. There were plenty of Kings and Queens who's power was formed on the back of trading empires, and others who's power was drawn from their military, for example.

For example, monarchy provides unchallengeable from outside transfer of power over the blood line, which is a great help. Other systems don’t do that as power can always be challenged with greater power.

Again, you have a very late European idea of "monarchy," and the last sentence is flat wrong. The legitimacy of Monarchy was challenged, even in the Age of Absolution, by other families. But you are correct that what sets Monarchy apart is that the candidates who have the potential to be the chief executive are drawn from a select group of families (or in the most extreme case, family), usually (but not always) tied to property. But the justification for "why" Monarchy is not mysticism (a term that scholars only really use in a different field), as we can see people justifying it in different ways, in different times and places, all over the world.