Microbiological research is no different than other types of research in other fields: you want to isolate variables and end up with one, specific final goal.
In microbiology, sample cultures are affected by a variety of conditions such as:
But during research, the goal is to keep bacteria separated by microbiological species, leaving one of a single species as your focus. This is the pure culture. The pure culture can then be used for further studies where it can be put to a series of different tests that aim to understand how that specific species survives or adapts to a myriad of variables, tests, control groups, and other scenarios.
The importance of having a pure culture, and not a mixed culture, when performing biochemical testing is that a pure culture may react much differently in isolation than when it is combined with other species. Bacteria replicates at infinitesimally long rates and one species may enforce or weaken the other. Other species can even co-exist. But if a scientist wants to focus on the biochemical reactions of any culture, a mixed species culture will invalidate and eschew the results of the experiment. A mixed species entails contamination and, as such, the control of the experiment is lost.
Biochemical tests help to identify a certain disease and they are based on the biochemical characteristics of organisms. For example, if chemical reactions, in our body, does not correctly occur, some substances cannot be produced or its levels are reduced. Biochemical tests can detect these levels disturbances such that the specific disorders can be diagnosed.
If the culture is not pure, it is impossible to detect the different types of the cells because its morphologies are alike. Since the identification process of different types of cells is not possible, then the result of the biochemical test is not accurate.
Hence, the reason of having a pure culture instead of mixed culture is that the accuracy of the response to the biochemical test performed.