False positives are the main problem here, exactly. We'd all feel a lot better about facial recognition technology with police reform that ended/compensated the widespread harm being done to mere suspects, as well as fixing courtroom standards of evidence to take into account that things like facial recognition are essentially pulling signal out of noise. If facial recognition turns police onto a suspect who is then found to possess the stolen items, the latter is corroborating evidence that they've found the right person. If facial recognition turns police onto a suspect who then merely looks like what eyewitnesses remember, that part of the witness's recollection is inherently correlated to how the suspect was picked and so it needs to be disregarded.