Maybe it could be better phrased as, "Democracy is better than autocracy, and we think it's crazy to try anything else".
There is certainly in a lot of room for improvement in how we elect leaders and what powers we give them. But, I think the evidence overwhelmingly suggests that dispersed power is better than centralized power. Remember that humanity has in fact tried a lot of variations of democracy and government throughout history. None of us actually lives in a direct democracy today a la ancient Anthens, we live in republics.
To reiterate, my main objection to asserting "democracy is the best" is that it discourages thought about other possibilities.
I don't know what work better. But I do think there are other possibilities. I'm using a somewhat stricter definition of democracy and autocracy. For our purposes, lets say a democracy allows nearly everyone to vote for a person or party that will have complete or nearly complete control over the government. We'll allow exceptions for felons and young people not voting. Lets call countries where one person has full power an autocracy.
I'm not going to give an example of a perfect form of government. But I'll give some bad or half-baked ideas just to illustrate it's possible.
As you mentioned, there's anarchy. Not far from there, you could have rule by corporations, where corporations hire their own internal police force to protect their employees, enforce their rules, and make up for the lack of national government. I know, scary. I said these weren't good ideas.
You could have rule by experts. Technocracy, or something similar. Only economists would vote on economic policy, medical professionals would vote on healthcare policy, etc.
We could say all new laws must be in pursuit of some mandate, such as increasing standard of living for the lowest 30% of the population. Laws that don't work towards this goal could be challenged and struck down in courts. Maybe laws could be proposed by anyone and the most upvoted ones would be considered by the courts.
Maybe direct democracy should be revisited now that we have the internet.
We could allow more departments to operate independently, much like the Federal Reserve Bank does now.
Maybe it's totally impossible to improve on the democracy we have now. I'd still rather not discourage thinking about it.
* No votes, just voluntary interactions
* The people voting on every issue
* The government/representatives being chosen randomly from the people
* Elected representatives being voted for by the people
* Political parties being voted for by the people
Then you have more details like franchise, denizens vs citizens, bicameralism, and more to worry about.
I would also say China today is neither a democracy (as least as you would think) or an autocracy.
China's a pretty interesting counter-example. I don't know very much about their government unfortunately, beyond what tends to make the news.
There are dozens if not hundreds of different types of democracy, each with its own set of advantages and disadvantages, and many forms of democracy that have not yet been tried. Most of them would be disastrous, for example "direct democracy" as opposed to representative, parliamentary democracy could not possibly work outside of a small village.
But it's odd to look at this as trying something out. As far as I know, no political system has ever been tried out. Okay, maybe you could count the genocide in Cambodia by the Red Khmer as trying out, but even they didn't really have the intention of just "trying out" this new, accelerated path to communism.
Political systems are put in place by emerging elites after a disruptive event (e.g. revolution, war, cataclysm, mass exodus) has taken place.
My objection to refrains along the lines of "democracy is the best system" is that it tends to shut down thought about other possibilities. We were taught from the time we're young that democracy is the best. But in reality, there's been very little experimentation. I'd rather encourage people to think on how we can continue to evolve our forms of government, not just in the details, but all the way up to how we choose our leadership.
I don't know how we'd test them. Computer models? Trial runs in small communities?
I don't know if anyone will come up with anything better. But there are possibilities other than "everyone votes for a leader" or, "one leader has power for life".
Democracy can be damn scary sometimes. The Nazi party was democratically elected. Who's to say that in 20 years, the majority of Americans couldn't be bigoted against some minority?