Why do we bother with recounts?

When looking at elections we often have “mandatory recounts” that are triggered in a close race. Now, I’m all for ensuring that all ballots are counted and that priovisional or otherwise questionable votes are given the consideration they are due. What I don’t understand is this fetish for recounts “to be fair”.

There is nothing special about recounts – they’re simply another count of the existing ballots. It is known that some fraction of votes can be damaged in a recount (depending on the ballot technology), and there is nothing in a recount that avoids the inevitable (if small) errors that can occur with even the best technology.

So why do we bother? Why substitute a second count (often with a less reliable method such as hand counts instead of automated counts) when effectively you’re just throwing the dice again and hoping the random errors come out the same? It seems it would be easier and less contentious to simply say that there’s one count that gets certified, and further challenges need to prove that there was a significant error in the existing count to justify reopening the results.