This may be a bit late in the discussion, but one of the biggest deal with allowing DNA to be put into databases which the police can trawl is that the risk of false positives increases as the database size increases. DNA profiling is a probability game with an underlying assumption that people in the DNA database are of higher risk of being guilty than those not in it. Most conviction on DNA evidence also use partial DNA, meaning they accept an even higher risk of false positive. The current methods in DNA forensic is also to use AI to combine multiple partial DNA to create a single profiles, and the false positives of those are not very well understood by judges and juries.

The legal system and the evidence value of DNA profile could adapt to a world where every persons DNA is accessible, but it is a slow process and I doubt it will be done in my life time.