Rhetorical: Here is Alma's conclusion. The points out that they have been delivered out of these bonds (the "bonds of iniquity" in verse 12) by God. Thus the king led them away from God, and God has led them away from a king.
As a final logical argument, Alma is saying to his people that since God lead them away from a king who caused them to stray from God, they should honor this God by staying away from kings. When Alma tells his people "I desire that ye should stand fast in this liberty wherewith ye have been made free…" he is not contrasting kingship as political rule to democracy as political rule. He is rather contrasting the freedom of God to the tyranny of a king who did not follow God.
If Alma's concerns are so clearly religious, why does he focus those concerns on the person of the king rather than the righteousness of the people? Part of the answer lies in the intimate connection between the king as political ruler and as the anointed religious ruler. The king ruled not by election, but by decree which was socially presumed to have come from God. This religious power of the king is where the king has the ability to bring the people into the "bondage of iniquity."
It is also quite probable that while Alma has in mind the recent example of Noah, the people may have known many other "kings" in the land - those who were kings over Lamanite cities. The organization of larger communities would be structured under kings, and that system would carry with it certain social expectations.
Indeed, the best explanation for Noah's excesses is that he was mimicking the social style of other kings in the area. Thus for Alma it is not simply the person of the king, but the entire developed social, political, and religious ideology that had become identified with the kings the people knew. His fear was that should they adopt kingship, they would also adopt the trappings of kingship, which could first lead to social stratification (Alma's first reason) and perhaps to the erosion of their religion (Alma's second reason).
Mosiah 23:14
14 And also trust no one to be your teacher nor your minister, except he be a man of God, walking in his ways and keeping his commandments.
Further evidence that Alma's ultimate concern about kingship is religious comes in this extrapolation of the principle. In addition to eschewing kingship, the people should not suffer teachers or ministers who were not followers of the Gospel. While the office of king carried with it dangerous connotations, it was the reality of the teaching that was even more dangerous. Therefore Alma counseled his people against allowing teachers who would not teach them correctly. This is the ultimate danger, that they might loose the position before God that they had recently gained, and to which they had committed through their baptism.