How much have you investigated the legality of this? In the EU biometric data is 'special category data' under the GDPR [0] and can only be processed in very limited circumstances unless you have the consent of the data subject [1]
Not only the EU, but you will have to check with each of the 50 US states as they all have a patchwork of laws. Illinois was one of the first, but I don't know much about it; I thought I read it was pretty extensive to the point some facial recognition companies specifically exclude it. Texas also has its own version as well, that I know of; again don't know details.
The GDPR works on the personally-identifiable vs anonymous distinction. Private vs public doesn't really factor into it, or at least only becomes relevant in the nuances.
Personally identifiable data is just a mouthful, which is why people like to misleadingly shorten it to private data.
I will contact my lawyer and double check this.