Why would we need one?

The Church Turing thesis is about computation. While the human brain is capable of computing, it is fundamentally not a computing device -- that's what the article I linked is about. You can't throw in all the paintings before 1872 into some algorithm that results in Impression, soleil levant. Or repeat the same but with 1937 and Guernica. The genes of the respective artists, the expression of those genes created their brain and then the sum of all their experiences changed it over their entire lifetime leading to these masterpieces.