Why is libertarianism so infallible?

It is due to it being the application of political science. It does not permit failed policies to be continued fruitlessly year after year with idealistic fervour, it is next to impossible for anyone surrounded by fierce libertarian critics to continue clinging on to lies. It is a purely functional machine, lubricated with justice and fueled by free speech.

Walls, or posted guards, or a number of other things. There's also the matter that those who commit violent crime are either insane or desperate, and the aim of anarchism generally includes removing the causes of such people's desperation. The rest could probably be treated, though it would likely require some form of coercion to do so.

Also, I agree that shared property is highly unlikely to work out; however, it's also never actually been tried. I'm much closer to Proudhon's model of a society where property is consensually laid out between all members of a society, but honestly even most people I know who want property eliminated don't really care about things like houses and toothbrushes.