I understand your point. When the classical gold standard was still in effect, though, there was no need for a global authority. Most everyone agreed that it was the best system possible and honored its obligations.
(2),and most of the world's mineable new gold is in countries that are corrupt and unstable (South Africa) or corrupt and unfriendly (Russia).
That doesn't matter. The amount of gold the people of a particular country own only serves to control the pyramiding of paper money from it. One gram of gold is enough to underpin a stable currency for an entire country if its leaders are committed to it.
Moreover, even then, the gold standard and the related use of silver as specie at times forced Britain into what in retrospect are odious decisions and policies. For example, a principal cause of the First Opium War (1839–1842) was that the Chinese imported little and insisted on silver as payment for their exports of tea and porcelain to Europe. This precipitated a decline of gold and silver stocks in Britain and Europe.
The remedy fashioned by the British was to force China to admit opium as a trade good. Soon, the demand for opium from millions of addicts in China was enough to reverse China's accumulation of silver.
The crux of the problem is that under the gold standard, shifts in national gold reserves impact the supply of money in circulation, which in turn affects the wider economy. It cannot be assumed that shifts in national gold reserves will always be managed wisely.
Notably, there is a line of reasoning and evidence that attributes the severity and worldwide scope of the Great Depression to a policy of gold accumulation by France and, to a lesser extent, by the US, without equivalent new issues of national currency. The result was that the supply of money declined as well, which prompted a decline and then a collapse in world trade.
On balance, the gold standard offers a critique of our current monetary system and a hedge against it but not an alternative to it.