Q: Why does Chinese culture seem to have so little influence on western countries?
A:
The influence of Chinese culture is so large people take it for granted. If one visits any palaces in Europe, say the Palace of Versailles, one cannot escape seeing the beautiful artifacts of china.
Niels Bohr led the Copenhagen interpretation of Quantum mechanics. The scientists were puzzled about how to comprehend Quantum mechanics. Niels Bohr solved the problem because Niels Bohr had his philosophy influenced by Taoism.
Chinese foods are part of American culture. Tofu is a Chinese invention. When it rains outside, New Yorkers would like to order a Chicken Noodle from a nearby Chinese Restaurant and have a cup of tea, which is Chinese culture. Jewish Americans would like to go to Chinese restaurants at Christmas.
Our world is connected by trade depending on shipping by sea. All the ships are built with separate sealed compartments, an invention of China. All the cargo ships use real control, a Chinese invention. Ship navigation using the compass, a Chinese invention.
The only difference in Chinese influence is that China did not invent Intellectual Property Rights for their inventions of paper, printing, tofu, the compass, and shipbuilding. We enjoy the influence of Chinese Culture without feeling its existence.