Shakespeare remained a popular mainstream playwright for more than two centuries throughout the English-speaking world. It was only after about the middle of the 19th century that this mass of cleverly bad language, sex, violence, and bawdy jokes that only linguists get (because nobody else knows what all the archaic words for genitalia are) was inexplicably relegated to being only for cultural elites. (Although I wonder if the reason we consider him so important isn't that we just don't have many plays from other authors in this era. He had rich and powerful friends, who decided to publish what we know as the First Folio, containing most of his plays, shortly after his death. A few decades later when the theaters were closed by Oliver Cromwell and the repertoire was lost, most of Shakespeare, except for three plays preserved elsewhere and two that have been lost, was safely in the libraries of many people who were in a position to keep their personal possessions safe from the sort who like to burn books.)
Classical music and opera were also intended for the general public, and are today seen as the height of elite, high-brow culture. They also used to be things that could make some serious money, like you can with good movies and TV shows today. And there ARE good movies and TV shows, just not very many of them. And, as always in the past, you start with good writing, or you get dross, no matter how good the acting, directing, sets, costumes, props, and effects are. Audiences have demonstrated an almost unlimited willingness to accept everything EXCEPT the writing being bad.