Even if the goal is a cultural appreciation, Shakespeare's plays will tell you as much about England in 1585-1613 as Terry Gilliam's filmography does about the Anglosphere in 1971-present.

It's more than zero, but it's also missing the overwhelming majority of the context and the world in which it exists.

Modern readings treat Shakespeare with excessive reverence: not just "a playwright" but "The Bard".

Those plays were made to be performed with very short rehearsal time before performing, outside, with no lights (at most fire, but it was wood and thatched and burned down from a theatrical cannon), in a crowded venue where audiences would be expected to jeer and cheer, whereas today it's a finely rehearsed performance by people who take it seriously performed for an audience who consider it high culture.

Monty Python's Gumbies aren't well understood by new viewer today, as modern news treats "the man on the street" somewhat differently than in the 70s. How wrong do modern viewers comprehend Shakespeare's characters, considering that "The Taming of the Shrew" is classified as a comedy?

That said, I was also busy teaching myself a lot of maths and science ahead of the classes; what I learned from school but would not have taught myself was the basics of German and French (though only the former stuck with me), the absolute basics of music notation, some metalworking and woodworking, and PE.

Oh, and the practical experiences in the chemistry lab, though I'd have still done the theory myself without that.