I'm asking why all of the arts associations say public funding for the arts is a necessity.
Because there were two types of art in history.* Craftsmanship, which was simply being the best mason, or blacksmith, and art as we know it. In the past craftsmanship as art was usually the best most people could afford, they'd in some way acquire a magnificient piece of furniture, or a great saddle for a horse. It might have been because they knew the craftsman or were owed a favour, or it might have been because the craftsman was simply inspired. However this craftsmanship did extend to some of the finer arts, storytellers or musicians would compose work and travel around jobbing. They'd want to, but would never really expect to become true artisans. A painter might make simple works for cheering up homes, or representing families, but they'd never, or rarely be the true masterpieces we recognise as art.
The other form of art, as we know it was for the rich. Patrons who could afford to pay the best to create the best. This was the preserve of the rich, and although it would funnel down to the lower classes, it was because of the rich that it was propogated.
Why do we pay taxes you ask? First it was protection money, to fund wars and armies and the parties of the nobles, but then it was recognised that some of the charities private citizens with more than they had to survive engaged in were also beneficial. Beyond the preserves of practicialities that were needed for the actual commerce, and thus lifeblood of a society. However, this is where a big "left v right" divide comes up.
Some would maintain that both the charity and practical aspect comes into the funding of art. Still others would maintain that art is owned by the people themselves, the nation (but this in general can be boiled down to charity vs practicality.) The idea that people of a country can be benefitted by art, affecting gross national happiness, or gross national enlightenment if you will.
I suppose it's collective bargaining power. I couldn't afford to get a top musician to write me the greatest song in the world, but collectively we can. This all relates to ownership of the art though (and copyright has developed as an ancialliary to that.)
People would still make art, but the nature of art is that it contains something of value to the human spirit. Naturally the rich would buy this. (Although of course some artists would hold out for what they see as integrity and only sell for the bare minimum for them to continue producing.) Unfortunately, we buy and sell things. And the reason art gets public funding, and why public funding is needed, is to keep it at the levels we appreciate, and for the people, in general. Because the diversity of art is publicly funded, simply means that art can remain of the public. However, it is not needed for art to continue, it's just that it raises the form of it. Craftsmen will always exist, and the pure arts will always exist to some degree because people enjoy themselves. But for levels we appreciate, which I presumed was couched in what you were saying in the first place, we need public funding.
*This is just from general reading and 101 type courses at University. I don't present any of this as expertise.