Look at how quickly the cops tracked Luigi Mangione. It’s not clear how much face recognition (as opposed to manual search) contributed to that, but even for a person who wore a mask, all it took was a slip up where he took the mask off in one place.

I am not saying this is a bad thing in the case of a pre-planned murder. But it does make it obvious how hard it might be to evade notice in the future, assuming you are doing it for more legitimate privacy reasons.