Why did European nations agree to follow the Open Door policy proposed by the U.S?
Most scholars believe that the Open Door policy that the US proposed had very little impact on anything. The European nations never really agreed to it in any formal way. To the extent that the European nations agreed to the policy, they did so because it was a way of reducing conflict between them.
During the early part of the 1900s, the major European nations had more to worry about than spheres of influence in China. World War I was rapidly approaching and European nations were more concerned with affairs closer to home, both in Europe and in Africa. Because of this, it was not worth their while to come into conflict with the US or with each other by trying to expand their control over "their" parts of China.
So, when the European nations eemed to be agreeing to the Open Door policy (and remember, they never did so formally), it was because it was in their interests to reduce conflict in China so they could concentrate on the problems brewing in other, more important, areas of the world.