Fascinating article showing that even in ancient times, and despite taxes, subsidies, trade-agreements, etc. trade between parties has always followed its own natural rate. So as much as politicians and various special-interest groups want and claim to "control" imports and exports, history shows it's futile.
I have the feeling it's not about politicians and special interest groups that try to claim control, but rather any institution (including the traders themselves). Often those instruments of governance grow out of those that control -- the Hanseatic league is an example of traders who eventually established their own laws to protect their own trade, and those controls became the governance that tried to stifle competition.
I think 'regulate' tends to be tossed in to the realm of 'government', but it's really humans who seek to embetter their own position. Apple's 30% cut on the app store is, in one light, a form of taxation. Commerce is a treadmill of people attempting to tax and rent take, and when fully successful become no different from the systems of control they once tried to circumvent or work around.
It's much more akin to convergent evolution than any "natural state" of markets. People design comparable instruments to solve comparable problems. It does not mean there is no design. Just like dolphins and sharks having evolved fins separately does not mean that there is a "natural law of fins", it means fins are pretty good at solving the problem they solve.
Eh, what. If governments have wanted to limit or curb trade or raise tolls - they have usually done so and the patterns of trade have followed the imposed restrictions. Google mercantilism for an example.
I have no idea what else this 'trade beyond government control' would be except smugling and black markets.