(Libertarianism isn't anarchy. If it were, we wouldn't need a separate word.)
Not that your conclusion is wrong, but if that argument worked we wouldn't need the word "synonym."
Although, the last hardcore libertarian I talked to suggested private contract enforcement, and I think I know where that leads- less civil suits, more broken kneecaps.
Unlikely, breaking kneecaps is manual labor that scales poorly.
In a short period of time abstraction layers would likely be built up to insulate creditors from the hassle of breaking kneecaps themselves. Debtor Prisons would probably arise, and with the realization that debtor prisons are not the most efficient way to extract an owed debt, debtors would be given the opportunity to agree to structured repayment of debt. Confiscation of property and/or the threat of imprisonment (backed by threats of violence that would rarely actually need to be carried out) would be used to enforce these repayment agreements. Hmm, this sounds familiar.
It's basically just a very round-about way of disassembling the current government and creating a new identical system that goes by a different name.
It concerns me that the Federal government is all our eggs in one basket, and people don't realize that doing dumb shit like blowing billions of dollars on programs that shouldn't even exist jeopardizes the whole basket... if our overbloated, overextended government collapses (and there is NO NATURAL LAW against this), it won't just take out the bloated overextended bits, the whole shebang goes down.
Sometimes people try to fling the "Oh, so, what about Police huh, you crazy libertarian?" at me, but at times I feel like I'm one of the only people actually taking the idea that government has certain core responsibilities seriously. Yes, we need police! Stop endangering them by stuffing every crazy-ass idea you come up with and decide call a "right" suddenly into the Federal government, without any apparent limit until it topples over!
We need to approach government more like engineering and less like a laundry list to the DC Fairy of everything we want in the world. One of the cores of any robust system is simplicity.
Anarchism makes sense to me as well, so long as that particular flavor of anarchism recommends that certain useful roles of the government be replaced by novel constructs, not merely eliminated. An anarchist who advocates for the elimination of contract enforcement is being shortsighted, those functions are useful to creditors and, if dismantled, will be recreated.
Slandering libertarians by asserting that they are the later form of anarchist seems to be a popular internet passtime.
The lay meaning is more akin to "chaos" or "disorder".
An-archy comes, literally, from "no ruler" or "no hierarchy". There are numerous definitions but it's best understood as an order arising out of interactions among equals.
That to my mind is its key disadvantage: there are no equals, and in the Libertarian context, there's a vast overt blindness (which I suspect is a covert strategy) toward the power which accrues from wealth.
Noted by Adam Smith himself: “Wealth, as Mr. Hobbes says, is power.” (Wealth of Nations)
Disclosure: I am neither an anarchist nor libertarian.