On the first question: Why did China take the classical Chinese exam?
Because classical Chinese is an important part of China language.
Since written records, the history of China has been handed down in the form of classical Chinese. If you don't know classical Chinese, it is difficult to overcome the language barrier of learning and understanding history.
Secondly, modern Chinese did not come into being out of thin air. It inherits ancient Chinese and classical Chinese. China users who don't know ancient Chinese and classical Chinese will not become Chinese experts.
On the second question: why not use "try songs" or "try poems" instead of classical Chinese?
If it is a "song", it belongs to the category of music, not "China Chinese", and you can take other subjects.
If it is "poetry", it is only a project of Chinese. China Chinese should also be tested, but it can't replace the classical Chinese test.