The main reason why you need to use the header and footer in your document is to include the document title and page numbers. You have placed the document title there in order to make it look formal. Including the page number may also be a requirement depending on the type of document that you are making.
A lot of reaction papers would not require the use of a header and footer anymore but if the professor tells you that it is required, you will not lose anything by following the instructions. In fact, B is somewhat right as you can make your paper look more impressive but this is not your main goal when you are submitting the paper. It has to be formal and it needs to have great content.