Again, none of that requires a monarchy.
Yes, but the current system bears some resemblance to one, and the current system is the default system. What reason has Kakara to change it, and what influences are upon iher to change it to anything specific? I hope that you will forgive me for saying this, but this is looking a lot like a personal crusade. As Scion, Kakara does have great relevance to the governance of the population, but reforming the government is not her job, running it is. Her personal goal has far more to do with the issue of Saiyan temperament and culture, which are quite distinctive and would likely interact with familiar governments in ways very different to humans'. This really is an extremely minor issue as far as Kakara's foreseeable life is concerned.
The system was, and continues to be, some randoms deciding they should be in charge because they're the strongest thanks to accident of blood.
That is called inheritance. If you are opposing people granting power to their heirs, then I am interested in where you are going with that, but that practice is alive and well in all governments that I am aware of outside of small isolated cults.
The Lords are the strongest because they are the Lords, and have the means to grant themselves the right to strength. They are not Lords because of being the strongest, that is just a perception thing that may or may not be supported by inherited physical traits. On that note, Saiyans are probably going to be seriously strapped for magic-users for the foreseeable future.
Also, the system is collapsing right now. House Senzu has demonstrated an ability to rebel, even though they are actually loyalists no one knows that. That means the monopoly on force, which is always actually an illusion enforced by the perceived impossibility of defeating the system, is gone. Right now, the only thing preventing the strongest asshole from taking over is that the Strongest Asshole is already in charge and her name is Dandeer.
The Senzu can hide themselves because there is no large-scale magical community to oppose their stealth seals. Dandeer has power because she assassinated the society from hiding before they even knew that there was a fight. All of this is the direct result of Dandeer being a freak occurrence. Long before Dandeer was able to subvert the Gokus, she had already hidden that a larger magical community had existed from the entire populace. Her ability to affect a vast but individually weak community is far greater than her ability to affect singularly powerful individuals. A more community-focused government would appear to be far more vulnerable to her. Her motives were provoked by the leadership, but that was due to her being amongst the leadership, and could have occurred in almost any household.
This isn't a failure to stop a single powerful battle-maniac from deciding that they are tough enough, and pressing the entire population to "voluntarily" come along as cannon-fodder to wear down The Enemy for them, or be "summarily executed for cowardice". This is a situation of a single manipulation maniac being able to single-handedly overcome every wizard in the entire civilisation, and then moving up from there. Most nothing could have prevented this given just how absurd Dandeer's magical advantage was from the moment she was basically the only one. The isolationism made things slightly worse, but the system in place seemed about as capable as anything, short of an Orwellian nightmare, of stopping Dandeer from happening. How would any other system have prevented this outcome?