A coin flip is simple, decisive, and immune to political machinations. A proper probability estimate is not.
Further, if you truly believe in democracy, then a candidate with 49.9999% of the vote is probably nearly as good as one with 50.0001%, right? So the cost of an error is low as well.
OK, that seems reasonable as long as one is certain that it's 49.9999% rather than a loose standard of "pretty close". What you wouldn't want is to make possible for the clear loser in a 48% - 52% race to demand a coin toss. Or maybe you do:
by the precepts of your argument, maybe that would be fine.
I'm uneasy with the random approach suggested by the article for fear that a truly crazy candidate might win the lottery, but I'd be good with having all the candidates above some large baseline (say, 30% of the vote) get a proportional shot at the win. I think I'd probably want it to be proportional to the counted share even if there is a margin of error, though.
I'd advocate calculating the statistical margin of error [1] before the election (which might, in fact, be +/-2% if the election is small enough) and doing the coin flip if it's within that margin.
Further, if you truly believe in democracy, then a candidate with 49.9999% of the vote is probably nearly as good as one with 50.0001%, right? So the cost of an error is low as well.