Why does the NOAA require a permit to be issued to stream images of the earth?
It's not just streaming. It includes all mechanisms for taking images of the Earth from space and somehow having that imagery get back to Earth.
Why do these regulations exist? One reason is the 1967 Outer Space Treaty. This treaty, to which the US is a party, deems that governments are responsible for any and all actions in space. In particular, the treaty says that "the activities of non-governmental entities in outer space, including the Moon and other celestial bodies, shall require authorization and continuing supervision by the appropriate state party to the treaty."
Another reason for such regulations is that the US government has a vested interest in protecting national security and in preventing international incidents. Imagery captured by an unscrupulous, unregulated company could easily threaten national security or provoke an international incident.
Why NOAA? IN 1992, the US Congress assigned responsibility for licensing private remote sensing space systems to the Department of Commerce, which in turn assigned responsibility to NOAA as the part of Commerce that came closest to having expertise in this area.
Why SpaceX? NOAA issued a statement on the broadcast of the SpaceX Iridium-5 launch. The second paragraph in that statement is key:
Now that launch companies are putting video cameras on stage 2 rockets that reach an on-orbit status, all such launches will be held to the requirements of the law and its conditions.
This appear to me that somebody at NOAA belatedly realized that second stages of commercial launches, with the second stage outfitted with cameras whose primary intent is to observe the spacecraft itself, nonetheless qualify as "private remote sensing space systems" should the Earth come into view. The regulations NOAA is required to enforce deems any private space operation that captures imagery of the Earth in any form to be a private remote sensing space system. The resolution or the quality of the captured Earth imagery is not mentioned in the regulations.