It depends on the use case. Example: I walk through the airport and an application scans my face and either calls security because I was recognized as a known terrorist or let's me pass because I'm awesome. The parent's point matters for what happens after. In the not a terrorist case the problematic system would retain that (it thinks) you walked through the airport. In a even more problematic system you now get ads because you were there.
Wait - wouldn't you _want_ the system to retain that information in your first case if you were mis-identified as a terrorist? I.e. you were recognized, but you were confirmed not a terrorist - so you won't be flagged later. Or maybe I misunderstood.
Otherwise, you run the risk of not updating the model to fix the false positive, and you might be flagged multiple times in the future.
I wouldn't want the system to keep information about me having been anywhere unless I'm a criminal. How would that information be helpful in updating the model. It already worked correctly.
Wouldn't the analogy be like Facebook identifying your face in photos, but not retaining the fact that you're in the photo?