In the United States, the Freedom of Information Act (FOIA) allows the public to obtain copies of information from the executive branch of the federal government. Most state and local jurisdictions have similar laws.
There are exceptions to FOIA requests, one of which is if disclosing that information would result in an invasion of privacy. Recording license plates at a public intersection is not an invasion of privacy. That is the entire point of a license plate -- to be able to publicly identify a vehicle. Neither is taking pictures of people in the public space.
There are other exceptions, such as in the interest of national security or during a criminal prosecution if releasing that information could interfere with the case.
It is up to each jurisdiction how to provide the information. For instance, the clerk's office might allow you to peruse their birth/death records in person. In other cases, you might have to submit a request in writing and receive the information at a later date.
The jurisdiction may charge a reasonable fee for obtaining the information, representative of the effort needed to produce it. Fees are waived for news media.
So, yes, anyone can get copies of city surveillance video, although it may cost you to obtain it.
If a jurisdiction claims a "policy" of not releasing such information, your recourse would be in court.
A grey area might be information the government never had in the first place. For instance, if they were leasing traffic cameras from a private entity that views the images and only forwards potential violations for possible prosecution. If you filed a FOIA act for ALL footage or LPR reads, the government could argue it cannot release information it does not have.
This issue was central to the Hillary Clinton email scandal. The response to a FOIA request for her email regarding Benghazi was "no records responsive to your request were located." This was because the government did not have her email, which was on her private server instead. The story goes on from there. I am not trying to argue the scandal in this post, but merely giving an example of where a FOIA request might be denied.