A better solution is to use better statistics.
If you think you need to collect redundant extra data about innocents just to improve inferences using the data you have, you're doing statistics wrong.
This has come up with DNA databases too.
Prosecutor's Fallacy:
https://en.wikipedia.org/wiki/Prosecutor%27s_fallacy
https://www.cebm.ox.ac.uk/news/views/the-prosecutors-fallacy
"The Prosecutor’s Fallacy is most often associated with miscarriages of justice. It’s when the probability of innocence given the evidence is wrongly assumed to equal an infinitesimally small probability that that evidence would occur if the defendant was innocent. Consequently, highly improbable innocent explanations have led to the assumption of guilt,"