> Things like basic research, things like exploiting a limited pool of shared resources, things like schools and prisons - they all go to hell when you try to run them on free-market rules.
Research is done with money from profits; if companies weren't taxed so much they'd have more profits left to invest in R&D.
Public schools are a vehicle for government propaganda and the brainwashing of children. There, they are conditioned to obey, not to question, and not to trust their own thinking. Public education as it is is as much child abuse as growing up religious is; it teaches kids the truth is in others, and that they couldn't have arrived at true conclusions by themselves.
There are better ways to deal with crime than prisons. It's a strawman to counter anarchist views with "but what of the roads? and prisons?" as if those are the only ways to travel and to curb crime. Go back in history, there are several alternatives to these that do not necessitate the government. Of particular interest is Iceland in the 10th century, but that's really just one example. I wonder how much research you've done to conclude with so much certainty that those things "all go to hell when you try to run them on free-market rules".
Advertising is not money spent trying to one-up competitors (though it can be). It is broadcasting the existence of a service or product. It's not about converting others to drop their favorite brands (though it can be), but about letting others know you exist. How do you get people to know you exist without advertisement?
I'd also like to point out that although I usually enjoy your comments here, you're being extremely condescending to me in your tone. Examples: "pretty much [...] debunks your points", "a lot of dogmas that sound nice", "trivially easy to be shown false", etc. The reason I point this out is because I'm routinely downvoted for defending my side of the argument, when in fact we should be using downvotes for people like you that address others with contempt and trivialize their points.
To respond to a particular point,
> Not having to compete with anyone does not make a product cheaper, it makes it more expensive. Competition drives prices down. So the government having a monopoly over a service makes that service more expensive.
True in many cases, especially if you only care about end-buyer price, but false in others. Some things fail spectacularly when you make them competitive. Things like basic research, things like exploiting a limited pool of shared resources, things like schools and prisons - they all go to hell when you try to run them on free-market rules. Some would say medicare is another similar thing. The market price is not the only important metric; some others are: quality, accessibility, efficiency, externalities.
> Advertising is not a waste of resources, it is investment of resources - literally, money spent buying leads in order to try and convert them into customers.
Who, were you not to convert them, would go to the competitor. It's a total waste of resources - you spend money (and more importantly, fuel and man-hours) trying to one-up your competitor, he does the same; on average, you still get the same amount of clients, only both of you wasted resources on a stupid zero-sum game. You'd both be better off if you agreed to not run any more ads that it take for people to discover you exist; yet since you can't agree on that, you're stuck in a zero-sum game.
[0] - http://www.raikoth.net/libertarian.html