"without rapidly turning into free for all for all kinds if criminal gangs, warlords and tyrants."
Gangs = Police, enforcing licensing rules on lemonade stands
Warlords = Politicians
Tyrants = Tyranny of the masses can be as oppressive as a single tyrant. If 51% of the population decides that it is okay to steal half of your property, that does not make stealing your property moral. It happens though, and nobody even talks about it. It is just accepted as necessary.
You are forced to fund indoctrination of children by government schools else you be thrown in a cage. Once people accept that certain people in their society get a special pass on morality and are able to steal, kidnap, and even murder other people on behalf of society, your society will corrode. The initiation of force is immoral. If your society is based on the initiation of force, the expectation of virtue from that society is naive.
This is all the usual "boiler plate" rhetoric we constantly get from the anti the initiation of force Libertarians, but it's seriously flawed, since, for one thing it doesn't take into account the nature of mankind.
As you should know, the vast majority of ordinary people are good at heart. Though many are led astray or for many other circumstantial reasons end up doing bad things. However this doesn't mean the are basically bad people and for the most part can reform themselves or be reformed by others.
On the other hand we have a small proportion of people who are basically bad evil people. Sociopaths and psychopaths who steal and kill, slander etc. simply for advantage to themselves or even for enjoyment and have no sense of empathy or remorse etc.
These people are irredeemable and will always represent a serious threat and danger to any society unless they are forcibly prevented from carrying out their evil acts. Since force is the only language the respond to.
I'm never quite sure what Libertarians mean by "the non initiation of force" and I'm not even sure they know themselves. For example, in an Anarchical society, if there's someone living in an area who is known to be a murderer, who would do what about it, and how would they go about doing it?
But even before that. How would someone or some group go about establishing an Anarchical society in the first place?
Also all the complaints you have about the current system are not intrinsic to a Constitutional Republic per se.
E.G. the 51% thing is not valid since the Constitution (when properly implemented)protects minorities through the bill of rights.
The same goes for being forced to fund indoctrination of children by government schools.
Unfortunately the expectation of virtue from any society is naive, unless the UN-virtueous can be kept under control and the only way that can be achieved is through the use of force .