Courts are not solving math equations and despite the popular belief to the contrary, most lawyers and judges are not bumbling fools. But to use math as an example of why you don't need an "impractically high" number of witnesses:

  - Let's assume "reasonable doubt" is 0.1%, so you need to be 99.9% sure someone is guilty before voting them guilty
  - Let's assume a random witness to a random crime has a 5% chance of getting some material fact wrong through no fault of their own
  - Let's assume that if you are on trial, there is a 20% chance you are guilty, based on the assumption if you're guilty and know you're cooked you're more likely to plea out, so the people remaining at trial are the truly innocent, the guilty who think they can beat the case, and the guilty who are just rolling the dice.

You still only need 3 witnesses telling the same story to reach >99.9% assurance of guilt. The odds of an innocent person getting convicted with 3 witnesses under this standard is 1 in 8,000.

In reality, witnesses are probably more than 95% accurate with material facts, especially when these are collected in isolation at different times, probably by different police officers.

And if we're being honest with ourselves, a lot more than 1 out of 5 people on trial are guilty of what they're being charged with. The bar for a DA to bring charges is very high, their entire careers are based on conviction rate.