The starting point for responding to this assignment might be to deconstruct the underlying assumptions of this prompt. In essence, the prompt sets up a binary set of oppositions between easy and difficult reading, similarity with contemporary life to value to the reader, and "relevance" as a key value. One approach an essay could take would be to reverse these binaries.
Learning means exploring things that are new and difficult. A good analogy might be exercise. One could life a piece of paper 200 times and it would be easy and comfortable, but it would not result in gaining any muscle. Lifting a heavy weight is hard, but struggling to lift a 30 or 40 pound dumbbell will make one stronger. The very difficulty of the vocabulary and syntax of Shakespeare exercises mental muscles and means a student actually is learning something and developing new language skills when reading this work.
Similarly, if all one reads is contemporary familiar works, one is living in a narrow bubble and simply reinforcing one's existing presumptions. The very alien nature of the setting makes students reflect not just on the past but also on the hidden assumptions of the present.
Finally, the present is the product of the past. To understand contemporary issues like racism and relationships between Christianity and Islam, it is important that one knows their history. Reading Othello is a window into the history that affects current relationships between Turkey, Arab nations, and Europe.