SHORT ANSWER
Films at the time were generally considered to have little, if any, artistic value. Nor was it believed that they had any commercial value once they had been seen by the public. Thus, their only value lay in the materials and chemicals the film stock contained, a value which increased during the First World War when these and many other materials were in short supply.
DETAILS
As Pieter Geerkens emphasized in his comment, Melies’ films were not melted down for the silver. In her biography Georges Méliès, Elizabeth Ezra states:
In 1917, his business office in the passage de l’Opera was
requisitioned by the army, which seized approximately 400 films and
melted them down in order to produce a chemical used in the production
of boot heels – as has often been noted, this was a sad irony for the
son of a shoe merchant.
Celluloids, from which films were made until the 1950s, were used in the production of
celluloid dental plates, harness trimmings, knife and cutler handles,
emery wheels, brushes, shirt cuffs and collars, shoes, piano keys, and
a vast range of other items.
Source: Deac Rossell, Exploding Teeth, Unbreakable Sheets and Continuous Casting: Nitrocellulose from Gun-cotton to Early Cinema
With the onset of World War I and the resulting loss of industrial production and shortages of raw materials, requisitioning was common in all the European countries at war. Melies was by this time bankrupt and no longer producing films, his career derailed by his failure to adapt to changing tastes, the death of his brother and business partner, and a series of bad business decisions.
Photo source: cinemathequefroncaise.com Melies' studio in Montreuil was requisitioned by the French army in 1917 and turned into a military hospital. At the same time, about 400 of his films were melted down.
The other key point to note is that films, especially ones made for entertainment, were not considered to be works of art at the time. As Patrick Robertson notes in Film Facts, the archives and film collections formed before the war and in the 1920s
were generally concerned with the preservation of films as a record of
national or civic history.... The first National Film Archive formed
as record of the film industry, rather than as a retrospective of
public events, was...in Germany on 4 February 1935....The following
year, Henri Langlois formed the Cinematheque Francaise from his own
private film collection.
Photo source: Un homme de tetes, 1898. A still from one of the many trick films which, at the time, was not considered worth preserving. This 1898 film Un homme de tetes fortunately did survive. The film (about 1 minute long) can be viewed here.
Sadly, Melies had destroyed his remaining films in 1923 as he had nowhere to store them. Likewise, most American studios destroyed most of their silent film archives: they saw no value in them, celluloid film was dangerous to store (see, for example, the 1937 Fox vault fire) and the studios needed the storage space. Consequently, it is estimated that 75% of all American films made before 1930 are lost forever.
As with almost all other films of the period, Melies’ collection of studio-bound trick and scifi / fantasy films were seen to have little or no commercial value once they had been seen by the public, even though they were hugely popular in the late 1890s and early 1900s. There were no TV or cable companies these films could be sold to after their initial release.
Sources
The Film Preservation Guide (National Film Preservation Foundation)
https://www.theatlantic.com/entertainment/archive/2013/12/most-americas-silent-films-are-lost-forever/355775/
https://encyclopedia.1914-1918-online.net/article/raw_materials
https://theculturetrip.com/europe/france/articles/early-cinema-the-magical-world-of-georges-melies/
http://www.victorian-cinema.net/melies
http://www.filmsdefrance.com/biography/georges-melies.html
John Sedgwick & Michael Pokorny (eds), 'An Economic History of Film'
