It is not so pashut that the Torah or Tanach thinks appointing a King is a good thing. And, it does seem accurate that Don Yitzkak Abarbanel thought either we should not, or at least that we don't have to. I am not conversant enough in Hebrew to read the linked article about Don Yitzkhak's views, but R'Yehuda Nachshoni (trans., Shmuel Himelstein, Studies in the Weekly Parashah) writes:
"Abarbanel... Holds that Shmuel's opposition [to appointing a king] was the correct course to be followed, and there is no obligation to appoint a king. Abarbanel answers all the attempts to show the contrary, and also shows how the words of Chazal can be in keeping with his view." (p. 1294; on Parasha Shoftim).
R'Nachshoni's writing on this topic presents a lot of the arguments, and Don Yitzkhak's responses. It is under the heading "The Regime of the King and the Regime of the People" in the Art Scroll edition.
The OP's statement that "Because by praying you becoming a slave to whatever you pray to. But anarchism (except of some small branches) do not support master-slave relationships." is also not, I think, a valid objection. The central aspect of anarchism is lack of a coercive relationsip among humans. I don't think most anarchic schools of thought would call a "voluntary" decision to submit yourself to HaShem as a master-slave relationship.
The question of whether the mitzvah to set up courts is necessarily violated by anarchy is a more difficult question. But, one can again imagine an anarchist allowing voluntary submission to beis din.
Anarchy doesn't actually mean everyone just do what they want. This is a major misunderstanding. What it really means is lack of coercion and lack of hierarchy. Most anarchists imagine a world of voluntary association and mutual aid, and that seems to me to be very consistent with the Jewish worldview.
Rabbi J. Sacks has an essay in his haggadah called "Building a Society of Freedom." Judaism, R' Sacks argues, holds dearly the idea that we are all equal; we all have tzelem Elokim (I'm not sure R'Sacks explicitly makes that connection, but it seem obvious). He approvingly quotes Paul Johnson: "The Jews had this gift. To them we owe the idea of equality before the law, both divine and human."
But, he also argues that freedom is another central aspect of Judaism. We see this in Shabbos, Shmitta, and Yovel, where we see freedom in time; we also see it in the Torah's general concern for the poor. "A society in which the few have wealth" (and, I would add, in which the few have power) "and many are on the verge of starvation is not free by the standards of the Hebrew Bible."
I'm not saying that any of this proves that it is halachically acceptable to be an anarchist. Certainly the existing schools of anarchic thought -- and, more importantly, the society that has grown up around them -- may not fit in a Torah lifestyle. But, I think that one could imagine an anarchy that would be consistent with Torah. And, it very well may be that that is the preferred system.