I think that entry into some art places should be free, but I do not think that entry into every art place should be free. Everything starts with the rights of the artist who creates a work of art. The artist pays for the creation of that work of art through their efforts to acquire or create the raw materials and then their work to create the work by using those materials. The artist that creates the work has the absolute right to control what happens to that work of art, including whether or not other people can view that work of art and what conditions other people must satisfy as a condition of being allowed to view the work of art. If a community as a whole (a municipality, a county/department/province, a nation) chooses to direct its government to pay all of the costs of paying artists fair value for rights to control a work of art and all of the costs to build and maintain a place to display and protect those works of art, then the community has the right to determine whether or not some people may enter the space and view the works without paying a fee. In this case I think that the community has a moral obligation to allow all members of the community to enter the building and view the works without paying a fee. However, if a community as a whole is unwilling to pay all of the costs of paying artists fair value and the costs to build and maintain the space for protecting and display the works, then the only way for artists to receive fair value for their works and to pay the costs to protect and display the works is for an individual or a group of individuals to pay those costs. Those people who pay those costs have the right to demand some form of payment from other individuals as a condition for being permitted to view those works.

Yes, Galleries of art are important. Seeing different forms of art is good for each person so they appreciate their own lives, other people's lives and they can slow down to consider new ideas. I think visiting art galleries should be free or persons could bring an item in exchange for admission. Sometimes in the U.S. people bring a food item to be given to people who do not have enough food.

I think modern art is always important since it reflects the times differently than literature does. Should it be free? Personally, I think you should pay an entrance fee.