Also in the United States, you have the right to video-record anything you can see from where you are if you have the right to be present. You have the right to record any happenings on or in your dwelling and its curtilage. There is no question whatsoever that everyone has the right to mount a doorbell camera and do whatever they like with the recordings.
The only exception is that if you are not in a single-party consent state, you might not be able to record the audio. It is unlikely that a legally protected conversation would be happening in mic range of the camera, though.
We could, for example, make it such that you can continue to record, but that those recordings couldn't be used as input to facial recognition software without the consent of the person being recorded.
Just because you _currently_ can do something legally does not mean that it _must_ be that way.
You cannot abridge freedom of expression without an amendment. Nor can you abridge freedom of computation.
You should perhaps instead endeavor to strike down anti-mask laws as being contrary to existing freedoms. The logical counter to automated facial recognition technology is facial concealment practices. It is the least harmful to liberty.
Alternatively, we could all wear--with our masks on--t-shirts with other people's faces printed onto them (especially Batman's face). And we can, of course, ban the government from using facial recognition technology without a specific, limited reason for doing so.
Just because I can record you from my porch and identify your face as appearing often, doesn't mean I would be able to tie that image in to a compulsory national identity database with facial photograph data included. Individuals might instead be able to identify a face as "John Doe #154" on their own server, and maybe match it to "YourMetroArea Serial Package Thief #15" on neighborhood-watch.net . Maybe I can set up an alert if any of the shared criminal faces show up and get recognized, or I can voluntarily forward my video to the cops when an incident actually happens. Giving cops unrestricted access to everyone's raw feeds is a bad, bad, bad idea. You bring in the cops only when it is apparent that a crime has been committed, an identifiable individual is responsible, and there is now a tangible reason to deanonymize the culprit.
What's wrong with an amendment? I don't want to live in a world where I have to wear a face mask to get some privacy. And they will probably soon not even need faces but recognize you from your height and the way you walk.
Nothing, in theory, but I don't think any amendment can get enough legislature votes to pass and be ratified right now, and the Powers That Be are absolutely terrified of what might come out of a Constitutional Convention. Anything could happen: gun control, equal rights for women, gay marriage, abortion rights, a requirement that presidents must divest all businesses and show tax returns prior to inauguration, right to strong encryption without back doors or key escrow, technology privacy and personal data ownership... anything.
So then we'll need masks and privacy-enhancing shoes.
What if the camera field of view was strictly confined to a neighbor's front door and facial recognition was used to log every visitor; all of which was freely available on the internet to any person?