Your first sentence displays a misunderstanding of how probability works. It is not just as likely that it won’t even out in the long run. Unless there is genuine bias, random mistakes will tend more closely to approximate to a 50/50 split over time. Just as the proportion of heads and tails will for an unbiased coin. If you allow a long enough period of time, and the mistakes are genuinely random, it is not equally likely but vanishingly unlikely that they will fail to approach even.
Still better to get them right in the first place, though