The problem is that people who understand statistics can be told this, and will see the problem. The overwhelming majority of the public (and legislators) have little understanding of statistics, and are blinded by "even if it catches one criminal that would have otherwise been left to walk free and murder someone, it is a positive for society".
The only way people will understand why it is bad is for it to be deployed, and news stories to begin to come out about the number of people detained due to false matches, along with some high profile people in government falsely detained. Unfortunately at that point the money has already been spent, so the talk will be about how to fix it.
You can reduce the number of false matches to any arbitrary level by requiring a higher confidence of match, but that reduces the number of true matches to where it was never worth the money in the first place. Except to the company that got the contract, and the politicians who got campaign contributions from them or lobbying jobs from them after they left office. And that's all that really matters to the politicians - they aren't spending their money, after all.