The council is the people
The council, being a *public* body, just like any public body acts on behalf of, is funded by and exists solely at the behest of 'the people'.
Commercial use therefore is charged generally on the basis that a private business entity should not profit unfairly from the effort of the people expended for the benefit of the collective people.
Non-commercial use, of which the copyright laws generally cover with something equivalent to public domain categorisation, is normally given freely and by default because it is in a public space, i.e. a space belonging to the public - belonging to the people. If an artist has seen fit to have his work permanently placed within the public space, the space for the public, then that is exactly what they have - artwork in public for the public.
How many people that walk by the installation everyday see the work for free? Where is the difference when seeing it online? It is still seen for free in the public space, by the public.
Take an example: A man lives in a building beside a public square. As was puzzlingly popular sometime ago this fellow takes a picture of the same view out of his window every day and adds the still image to a video which is posted to, for example, YouTube (in this scenario the video never generates revenue). After sometime an artist paints one of the walls of the square that is within view of the photographers window. The man has not changed his actions he is still taking a picture of a publicly accessible, owned and funded space. The artist has imposed their art into the space either based on their artistic opinion or at the behest of a public body.
If the photographer continues without change who is at fault that the artwork is now in his YouTube video? The artist, the photographer, the public body or the public? If it is any of the latter three then if the photographer is charged it will effectively be the public charging the public to use a space already paid for by the public - which sounds pretty silly to me. If the fault lies with the former then would we have the artist remunerate the photographer? That would sound equally silly!
Corollary: This would only apply to fully public and permanent works and depend on the country's legal definition of 'non-commercial'