I don't think it has shown how flawed our political system is.
By its very nature, being PM carries with it the risk of destroying the whole country. By design, we are able to elect people who could in-theory take a course of action that literally wrecks the country.
It is meant to be up to the personal insight and suitability of the leader that they will not use this wrecking-ball capacity to do incredibly divisive things. David Cameron misused this power by holding a referendum that he knew was not defined, in which the course of action he wanted (remain in the EU) represented a certain course of action over which there was no ambiguity, whereas the other option he thought would never be picked (leave the EU) represented an absolute infinity of actions, most of which would constitute a gross act of national self-harm if we attempted to enact them quickly.
It is the ultimate moral folly of a leader to take a risk that might personally pay off for them, at the expense of the entire nation. David Cameron is a rich man, so it cost him personally nothing to gamble with our EU membership because it stood to secure him the role of Prime Minister, but should it fail he merely goes back to being an incredibly wealthy person. But loss for the nation means that we've become locked into a totally ambiguous, unenactable and highly divisive issue of nationalism.
This constitutional crisis doesn't represent a flaw in our system. The Prime Minister needs the power to create the crisis we're currently in, and the people who vote nationalistically and elect charlatan gamblers who create crises need to see the consequences of their little-Englander mindset.
Brexit, the resultant loss of our wealth, the resultant loss of our national standing, the years of political paralysis and the ongoing humiliation of watching attempts by Britain to throw its weight around fail over and over, are the philosophical reckonings that the racist little-Englanders who claimed they knew what they were voting for and strutted around squawking "you lost, get over it" deserve. Absolutely all of this is necessary, and it doesn't represent a flaw in our system. Being at square 1 3 years after the vote, begging for extensions and slipping further and further down the list of wealthy countries is the reckoning the fools who voted for Brexit need. This nation needs this humiliation to play out to its fullest, so that it becomes part of our national consciousness to comprehend the folly of nationalism. We are having the same reckoning the people of Germany had for their racist folly at the end of World War 2, at a fraction of the cost.
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