
Many of the problems in Alexandria are simple. There is no system, and there is no force that guarantees the power of the leader. Thus, Deanne’s power is fragile and via the free consensus of the majority. At any time, the majority could withdraw this consensus, and the society would immediately devolve into anarchy. The force that she does integrate as the executive is Rick and Michionne—the problem is they are not loyal to her. So, essentially, she brought in an armed force that had every incentive to take them over, especially since Alexandria is inhabited by people who do not know how to fight and are not hardened by suffering the way Rick and the others were.
The situation here evokes the concept of the monopoly of violence and civilian control of the military. The military is a kind of “shadow society,” with its own professionals, tradesmen, service people, &c., as well as its multitude of soldiers. Compared with the rest of the population, they are stronger in all possible ways. They are supposed to be. The problem is, if they are not under the complete control of the civilian population, then they could and many times do take over. Many parts of the world are under military control, juntas, usually as a result of a breakdown of civilian society but sometimes also as a result of coups or forced takeovers.

In a post-apocalyptic scenario, I imagine (as I’ve mentioned before) that the warrior class would take precedence over every other class, and the most successful societies would have a primarily militarized culture. The brutal realities of scarcity and the lack of widespread institutions upon which people can depend make that a necessity. As such, Rick was right to feel that Alexandria was primed for collapse. It had no way with which it could defend itself during a full-scale attack, which was likely given their prosperity. They would also at some point require more and more people to help with their increasing needs, which increases needs further necessitating more people still, and in such cases an internal security force would be needed to supplant the external force that protects from threats outside.
As a member of the police force before the apocalypse, Rick was very much aware of this. However, being the idiot that he is, he does not articulate it in any way that makes sense. Rather, he has a vague feeling that something is not right. Moreover, his attraction to a married woman was the ultimate cause of his outburst. The justifications regarding security were secondary.
At this point, these people were dramatically, irrevocably traumatized. They could not and never be expected to function in the heightened capacity that they had to in their given roles. And Rick and the others were showing signs of the disordered thought associated with PTSD, with Rick especially given his aggression. A person like Deanne should have been able to know this. Alexandria was therefore doomed to fail.

Carol in particular was very deeply traumatized. She has been so traumatized by so many different kinds of tragedies in her life that she has integrated her response to this trauma into her very ethos. She has purged herself of every caring instinct, and though in the beginning it seemed as though she was ready to return to a kind of suburban housewife mindset, we see later that actually it was a ruse that was part of her ruthless machinations.
Rick is a total loss. It strains belief to think that the people still consider him their leader, even after he makes such terrible calls, although we do see them beginning to realize that he may not be fit for the job. And as always it is Michonne who ends up knocking some sense into him—which in the case of Rick is knocking him completely out, since there was no sense left. I still don’t understand why she is not their leader.
The very apparent problems of societies like Alexandria I think are what rob these later seasons of drama, including the pacing of the stories that are simply too fast. We are not given enough time to care about these people. And with such a simple scenario without people that we can truly, deeply care about and understand the series becomes a series of events that, while titillating, and somewhat interesting, are still not to the level of storytelling that can be considered great.