I had the same experience reading A Midsummer Night's Dream in high school -- I could follow the story, but it was a slog to get through and I didn't understand what was supposed to be so great about it.
Then I saw an actual performance of the play recently, and it all clicked. It was just as understandable as any contemporary film, and easily one of the most fun and entertaining stories I've seen.
I gave up trying to read plays shortly after school. There's no point to me, they are supposed to be performed. I still think it's worth studying some of the more famous ones in school, but any study should absolutely involve actually going to see the play at some point.
I've had a similar experience, with the same play, but in an absolutely minimalist setting. No sets, the only props were a few chairs, and costumes were the same white slacks and smock worn by all the players.
And it absolutely worked.
This wasn't long after my secondary education --- I'd just started uni. But enough had happened that I got it.
As I've commented recently, even as an excellent reader, there's something that hits quite differently from hearing fiction (or even nonfiction) not just read but acted. Selected Shorts is an excellent source for this. See: <https://news.ycombinator.com/item?id=49163756>.