Having a wonder of the world can be beneficial to a country in two main ways. However, neither of these is a panacea for the country.
First, the possession of a world wonder can be economically beneficial to a country. This happens through tourism. An example of this is the Great Wall of China. This is, of course, a well-known world wonder and there are people from around the world who are interested in seeing it for themselves. This brings people from foreign countries into China as tourists and it also encourages people in China to engage in tourism. Both of these sets of tourists create more economic activity and China gains from that activity.
Second, the possession of a world wonder can be emotionally or psychologically beneficial. The possession of a wonder can emphasize to the people of the country that they have a rich past. It can make them believe that they are capable of great things since they are descended from people who created a wonder. This can lead to a greater sense of national pride.
Of course, neither of these things will solve a country’s problems. For example, other types of economically valuable industries are needed. However, the possession of a world wonder can be beneficial economically and psychologically.