https://en.wikipedia.org/wiki/Chad_(paper)#Partially_punched_chad

I don't know if you were old enough around year 2000 to witness this whole Florida recount debacle, "pregnant chads" and all that, but this was a good illustration why counting paper ballot is always imprecise, to some small degree. You can alter design of the ballot to minimize factor of randomness, and enforce some strict standards on canvassers, but it will never be zero.

The only ultimate solution here is electronic voting, where voter's intent can't be misinterpreted; however, in practice, people will never trust machines (even with paper trail), because "everything can be hacked". So we are stuck with paper ballots.

I mean, do you see an alternative? Every recount might change the result by a few votes, but we can't recount ad infinitum.

Mathematically speaking, with such a small difference, it's a draw. Neither candidate provably received more votes, but we have to select one. You can toss a coin (which is what they'd do if results were exactly equal), or stop after 1-st recount. Nothing is wrong with any of that.

Third count would very likely produce a different outcome, but the law doesn't require (or even allow) another recount.

Important part of orderly elections is finality. People vote, votes are counted, in some situation recounted, and that's it. Whoever won, won.

Before getting into conspiracy theories, do you have actual statistical estimate?

I mean, for example, in Poulos vs Morrison the total number of votes cast is just over 10,000. With a district evenly split across party lines, 1 vote difference isn't that big of an anomaly.

I am pretty sure your list of close votes isn't exhaustive, it probably only includes a few examples which garnered most publicity.

This would make an excellent ballot question.