"Private governance" is probably a better term to use for this than "anarchy."
Ed Stringham gives countless examples of private goverance all around us today and how is the primary reason for the order we see around us today: http://www.amazon.com/Private-Governance-Creating-Economic-Social-ebook/dp/B00XCTPVAU
I just finished reading Ed Stringham's book Private Governance: Private Governance: Creating Order in Economic and Social Life today.
The OP post reminded me of a point that he made repeatedly over the book: The idea the legal centrism is wrong.
Specifically, Stringham points out that even many radical libertarians seem to mistakenly believe in a kind of legal centrism. He writes:
> The approach of private governance stands in contrast to what Gallanter (1981) and Williamson (1983) labeled legal centralism, the idea that order in the world depends on and is attributable to government law. Legal centralism is widely held among lawyers, lawmakers, and even free-market thinkers who believe that “the protection and enforcement of contracts through courts and civil law is the most crucial need of a peaceful society; without such protection, no civilization could be developed or maintained” (Rand, 1966, p. 299).
> [...]
> One of the premises of this book is that just as one should not assume the effectiveness of governmental legal solutions, one should not assume the effectiveness of private legal solutions. Although not legal centralists in the traditional sense, many radical libertarians are legal centralists of a sort who simply substitute private enforcers for government enforcers of law. If a potential problem comes up, the libertarian legal centralist is prone to say, “That would be illegal in my ideal world.” Yet even the best private police or courts might not be able to solve a problem in a cost-effective way, so private parties may have to live with certain trade-offs or seek alternative solutions.
In his book, Stringham documents many ways that private governance brings order to the world other than a non-government private entity producing and enforcing a law in a legal-centrist-like manner.
So Stringham would say that the fact that the landscaper, mechanic, and plumber have a contractual legal obligation to you actually isn't of as great of importance as the legal centrists (including the libertarian sort) would have you believe.
Rather, there are all sorts of other private governance mechanisms that help bring people what they want. And they enable economic activity to exist in the informal economy, and black and grey markets.
So, taking this view against legal centrism I would say: The fact that the POTUS has no legal obligations to fulfill any of his campaign promises is not actually much of a criticism of the current system (contra what some of the legal centrist-like thinkers among us might think).