Why is it useful to a chemist to have a classification system for the types of chemical reactions?
It is quite useful to a chemist to have some kind of idea as to what to expect when delving into the unknown. Having a good background on compounds and elements and what they will do and what they won't do can be a great deal of assistance. Some of these chemical reactions proceed with relative calm. Others, like the mixing of sodium metal and water, can be quite explosive and dangerous. It helps to know what to expect.
I answered a young man's question last week about a chemical reaction involving potassium thiocyanate and ferric chloride. He was concerned because the instructions to the lab told him to record the color change that was produced in the reaction. He didn't get one, and wondered had he done something wrong. When you do the reaction described, the thiocyanate ion (SCN-) turns fiery blood red in the presence of iron ions (Fe +3). So knowing the type of reaction, and having some idea of what to look for, what to test for, can be quite helpful in dictating success or failure in the chemistry lab.