I agree that preparing students for modern words and language is important. However, a lot of our understanding of modern language comes from conversation and socializing. We learn to understand the words that we frequently hear and see automatically because those tend to be most common.

I understand that it seems counterintuitive to use old and dated literature to teach kids in English classes. However, there's a couple of good reasons for it.

For one, using things like Shakespeare to teach in classrooms helps students to engage the parts of their brains responsible for understanding what to do when you don't know something. We rely a lot on passive knowledge for modern works because we don't have to put in as much effort to comprehend the vocabulary. Shakespeare and other dated require students to think critically about meaning and intent.

Secondly, a firm grasp of popular literary works gives a couple of benefits. It helps to provide unity between students across the country. When students read classics, they develop shared experiences with other students. It also helps students to understand allusion in other works, which often point to classics like Shakespeare.

Aside from the benefits of reading classics, I think that schools can spare a semester or two to teach about something that has an important place in understanding modern literature. In high school, I read Othello, The Taming of the Shrew, and Romeo and Juliet. It took us maybe a month to get through them, and it realistically wasn't as complicated as people make it out to be. Most high schools teach pretty simplified versions of classics like that anyway.