The market actually does produce such things in some other countries. What the market does best is to allow people to create the wealth that will fund cultural activities. The United States has a strong tradition in which people who have done well in business support the arts. Names such as the Guggenheim Museum or the Getty Centre remind us of the generosity of rich patrons. Andrew Carnegie, who found fame and fortune in the United States, funded the provision of organs in many churches in his native Scotland, as well as numerous libraries.
In fact the arts have been funded by rich patrons through the ages. It was often regarded as a sign of good character and culture that a wealthy person would support art, architecture and sculpture. The emergence of modern economies since the Industrial Revolution has enabled wealth to be created on an unprecedented scale. This, in turn, has allowed some people to become rich through business and become patrons, where previously it was mostly aristocrats and rich merchants who could afford to do so.
When Kingsley Amis wrote for the Adam Smith Institute opposing arts subsidies, his central case was that if government through its arts committees funded the arts, their output would be skewed towards the desires and tastes of the paymasters, rather than from the passion and inspiration of the artist.
It must remain a suspicion that the committees responsible for handing out public funds as grants to the arts will give effect to their own tastes, rather than those which the public might freely choose to support otherwise.
Some arts can be self-supporting through ticket or admission prices, but government can help through its tax laws, remitting all or part of the tax that would have been due on money donated to artistic institutions. It does not itself need to dole out taxpayer-funded largesse, The UK's National Lottery has multiplied financial support for the arts without needing taxpayer funds. The view that the market cannot finance the arts and that government grants are needed to sustain them is simply not correct.