Unsolvable Political Problems Basically, the ordinary way to have political power is to organize groups of armed young men to fight for you. So, it seems entirely logical that the Founding Fathers wrote freedom of speech into the first amendment, and the right to bear arms into the second. Without at least the credible threat of violence, you can't force the government to do anything. But how will you threaten them if you're unable to organize, or if you are unarmed? And even if it doesn't get to the point of violence, how are you going to get support for an idea if you're unable to freely express arguments in favor of the idea? It is clear from this line of reasoning that freedom of speech is actually a political issue. Without freedom of speech and freedom of assembly, and without arms, you have no political power.
Libertarians often criticize government because it has a monopoly on violence. I think that's kind of the whole benefit of government, however. It is true that government is compulsory, and that it's generally incompetent. But in the case of choosing between the government and protecting myself from robbers without help from the government, there would have to be a very incompetent or malicious government in order for me to prefer facing the robber alone over having to pay taxes (it is actually getting to that point for me, but I'm not opposed to government in principle). I think the main benefit of government to individuals is that it has a monopoly on violence, which very likely means less violence overall.
I think the primary job of government is to limit freedom of action in zero-sum games (such as in murder or theft). Assuming that people are self-interested, and you stop them from competing in ways that are harmful to other people, then you don't need to know any of the details to know that the net effect is positive. This is probably why it became ubiquitous for governments to punish criminals, fend off foreign invasion, and not much else.
Pluses and minuses of different forms of government
Direct Democracy: By definition, it's not possible for a direct democracy to implement a policy which 51% of the people would be opposed to.
Limited Ruling Class (Aristocracy, Oligarchy, Republic, etc): If the ruling class has higher average political wisdom than the general population (such as by having higher IQ, or better education), then the government can implement wiser policies than would be possible in a direct democracy.
Monarchy: Monarchy is a simple and natural form of government. It is simple, because what is simpler than, "Person X is in charge"? It is natural, because power struggles tend to be unstable by nature, so that power becomes concentrated. The power being in the hands of 1 person is the natural result of power concentrating with time. Monarchy also has good incentives. The power and prestige of a monarch is the same as the power and prestige of his country. He is the owner of his country, whereas a president is a temporary guardian of an estate which he has no ownership in. The monarch is above bribery (what can you bribe him with that's worth more than the whole country?). The policies of a nation also tend to be stable over the life of a monarch. The line of succession is also usually clear in a monarchy, which reduces the frequency of civil wars.
The only downsides I can think of to monarchy are that it's arbitrary (why does having a great great grand dad who was awesome mean that you should be king?), and that in the case of having a bad monarch, the only remedy is rebellion.
Given the pluses and minuses of monarchy, it seems reasonable to me that it has been by far the most common form of government historically, but that dynasties do tend to get conquered from time to time and replaced by other dynasties.
Net Tax Payer Voting System: By definition, in a net tax payer voting system, it's not possible for 51% of the taxes to be involuntary. If 51% of the tax payers thought their taxes were too high, then they would vote to lower their taxes.
Military Service Prerequisite to Political Positions: This means, at least, that whoever is making decisions is not totally ignorant of military matters.
I understand that senators in Rome usually had military service. This has also been common for US presidents. Prussia, it was said, was a military with a state. Note that all these examples also performed very well militarily. It seems reasonable that governments with some connection to the military will tend to run their military better than those that don't.
It occurred to me while mulling over the net tax payer voting system, that a cryptocurrency with internal governance could be used to implement it (example are Cardano and Internet Computer Protocol). The government of a country could make a deal with some block chain (or a fork or derivative of some block chain), "If you vote to give us a 5% tax (or some other negotiated percent) on transaction fees and staking rewards, we will make your cryptocurrency the legal tender, so that all merchants have to accept it." This might be beneficial for both parties. The government would get voluntary taxes, and the government support would probably pump the bags of crypto holders. Because it's crypto, the vote could neither be rigged nor ignored. Whatever the results of the vote were would be automatically implemented, even if the government didn't like it. The government would be incentivized to try to protect the blockchain, and to convince tax payers and stake holders to increase taxes, hopefully at least partially by finding useful things to do with tax money. It seems reasonable to me that a majority of merchants might agree, "It is worth it to pay a 5% tax in exchange for having police, military, and a court system." But if there was something they didn't like, they could theoretically defund the government.
Currently, Cardano and ICP are run by stake holders. But it would make sense to tax transactions, which would be paid by merchants (such as by Walmart, if we were to transition to a crypto system). So, the block chain may want to create a special governance system just for taxes. It would seem fair to me if they hard-coded it so that the staking tax rate was always equal to the tax rate on transactions (or some fixed ratio), and gave everyone who paid taxes a vote on tax rates proportional to the amount of taxes paid. They might make the voting power decay with time, such that (perhaps) a dollar paid in taxes last year is as good as $0.50 this year. But the stake holders should retain all other voting privileges, because Walmart knows nothing about the governance of something like Cardano.
So, these thoughts lead me to the idea that it would be neat to have a government where military service was a prerequisite to having political power, but where the tax system was created bottom-up by tax payers through a crypto governance system. That way, the people with military experience would be the ones deciding what to do with the military, the people paying taxes would be the ones deciding how much they should get taxed, and the people who understood how money worked (they created a block chain and run it) get to print the money.
It seems reasonable to me that the only unique political idea I actually came up with was related to crypto. This is because crypto is new. People have been trying to run governments for a long time, and as I argue here, politics is a very difficult problem.