You're referring to various strains of anarcho-libertarianism, correct? I'm more familiar with geolibertarianism as a left-leaning libertarian faction, which doesn't have these stability problems, but does have a huge initial-conditions problem (it's nearly impossible to institute a land value tax in a society that doesn't already have one because of the effect it has on land prices, which are a primary storage form of wealth).
Yes, but those are the largest left-libertarian groups right now. I don’t think that Georgism would have these issues but you’re also correct about the difficulty of implementation. (It is garnering some interest in the UK, although I fear they will botch any implementation due to the immense power of the landowner class there.)