If the result is 49.999% vs. 50.001%, you cannot conclude anything meaningful about the will of the people. Maybe the weather was just slightly worse in a neighborhood supporting the losing candidate and it tipped the result slightly.

So even if the voting process is perfect, that close of a result is totally random for other reasons.

Most people don't seem to be capable of thinking about non-determinism like this, though. Witness the huge number of Americans who think the presidential election is illegitimate because Trump got 46% of the vote to Clinton's 48%, when honestly 46 vs. 48 is very little difference in terms of what they mean about the general will about Americans.

On the other end of the political spectrum, witness the amount of Brits who think a 52-48 vote to leave the EU is somehow relevant.

In calculus/analysis terms: this is why proportional representation parliamentary systems are better -- because the function from "how many people support which parties" to "what policies you end up with" is not discontinuous.

If the UK ran on a proportional system, they'd be getting some sort of very soft, Norway model Brexit. If the US did, a center-right Democrat like Clinton or Biden would be PM.

Routine double counting all votes would be controversial due to the high cost.