I think the reality is a lot less nefarious. They don't want your face. But they also don't care enough to not take your face. Why would Google spend lobbying and legal money trying to fight this requirement when it doesn't hurt their bottom line? On the other hand, requirements like storing ID cards does hurt their bottom line because it means:

1. they need additional security measures to avoid leaking government documents (leaking face photos doesn't hurt them as much) 2. not every person has a valid government document 3. additional customer support staff to verify the age on documents rather than just using some fuzzy machine learning model with "good enough" accuracy.

The bottom line is that companies are lazy and will do the easiest thing to comply with regulations that don't hurt them.