Well, of course they should. It's always possible that an impulsive child will touch a painting or sculpture without thinking, and it's always possible that the art work will be immensely valuable and need careful restoration.
But that very remote possibility is insignificant compared to the mental and emotional benefits that children get by experiencing art, especially from an artistic genre they're unfamiliar with - like abstract art or surrealism or cubism.
Galleries themselves usually give children a warm welcome and are happy to let them appreciate famous and valuable art works. They're very forgiving on the odd occasion that a child accidentally damages something.
Like the four-year-old boy who last year smashed a priceless 3,500 year old vase to pieces at a gallery in Israel. Far from being outraged, the Hecht Museum invited the child back to the museum with his family for an organised tour. And there was no question of the family being asked to pay anything towards repairing the vase.
In my experience gallery attendants are very quick to stop anyone (both children and adults) from getting too near the exhibits, so the chance of something getting damaged is pretty remote.
Pic: Gray, Orange on Maroon by Mark Rothko
