Keep in mind that comparing a DNA sample to a gallery for the purpose of large-scale matching raises the false positive likelihood significantly. I’m not at all convinced that this could be done without convicting innocent people.
Realistically I think the existing criminal justice system would be hard put to claim a wrongful conviction rate lower than that, so... I'm not sure this argument cuts the way you want it to. If you have a 99% accurate test of guilt, that seems like more than enough probable cause to continue investigating, and probably good enough to convict with just a little extra corroboration.
While there's a privacy argument to be made, I really don't think you're going to get very far arguing that this is going to cause quality problems. Frankly I think it's likely to help with reducing false imprisonment (i.e. by fingering the right suspect earlier, before the wrong one ends up in court).
So if you have a database of 10,000 people and 1.1% false positive rate, you're likely to get several false positives. Unless you stop searching as soon as you find a positive, of course...
If you're facing a jury (as you probably are in a criminal case) people have been convicted on far less than this with no other corroboration. It's all in the narrative put before the jury and their understanding of the evidential burden.
Some (older) types of tests might only compare a couple hundred locations, or not be particularly picky about how close a match actually is to be a match, etc.
And contaminated samples are a big problem