There's nothing stopping you from setting up a webcam pointed out your window. If you want to set up your own public-facing ALPR cameras, there's nothing stopping you.

Can I put cameras up on every street corner and on every traffic light? Doesn't answer my question anyways. I'm asking if the government via a third party can have this ability, would you have any objection to the entirety of the public from having this data and camera access? I'm assuming not since the people who advocate for this technology see nothing wrong with it.

If you do have a problem with public access to these cameras and tracking software, then it would be hypocritical.