Art subsidies are important for the success of the arts in the US, and its very important for a country to have a strong artistic legacy. The arts are the ultimate legacy in the memory of the world, and the art subsidy budget of most countries is already so small that cutting them would do little.
No, the arts would survive, even without art subsidies, because the public is smart, and would continue to support good art. Art, when it is subsidized, leads to a number of projects that the public is not interested in. A business person would not survive long making products that people do not want. People's demand would shift, and there would still be plenty of ways for talented artists to profit.