Everyone has studied shakespeare at some point in their life, whether it be school or own interest, but did Shakespeare have as profound of an effect on society at the time as he does today? Did students study his literature at their schools?
Shakespeare was influential among his contemporaries, but in his own time he was only one of many writers for the stage, rather than a landmark literary tastemaker or a figure whose works would be studied in schools. Far from being understood as timeless, Shakespeare was as subjected to passing trends as his contemporaries were (revenge tragedy, plays with Moors in them, plays with bears in them, plays with topical political material…) in a way that's not necessarily clear in a modern context. His own literary peers like Ben Jonson were comfortable criticizing him as grasping and coarse, more interested in stage bombast than factual accuracy or subtlety -- even as Jonson famously described Shakespeare as "not of an age but for all time". What kind of writers were understood as being writers for all time in Shakespeare's own day? Whose works were being studied and cited as examples of enduring poetic excellence in Shakespeare's own time?
When Jonson described Shakespeare as soul of the age, not of an age but for all time, Jonson was writing a fairly flattering retrospective on Shakespeare's greatness in the preface for Shakespeare's first folio. Left to his own devices, Jonson wasn't what you'd call an uncritical observer of his theatrical contemporaries; he knew Shakespeare's creative process too well to conceptualize Shakespeare as a monolithic literary titan, even as he was comfortable calling him a great playwright who deserves his contemporary fame. (And I don't think we have reason to doubt that Jonson truly did respect Shakespeare's literary achievements, even if he criticizes him quite sharply in some of his other commentaries.) In that same eulogy, Jonson namedrops English poets Geoffrey Chaucer and Edmund Spenser alongside ancient Greek tragedians Sophocles and Aeschylus, ancient Roman tragedians Pacuvius, Accius, and Seneca, ancient Roman comedic playwrights Plautus and Terence, and contemporary Elizabethan dramatists Beaumont, Marlowe, Lyly, and Kyd… it's basically a laundry list of literary greats as Jonson would have understood them. writers whose works would have been read and/or discussed at university level, with a side dish of famous contemporary writers who achieved commercial and critical success. Only Spenser and the contemporary dramatists could be generously considered "recent" at the time the first folio was issued.
Some of these names are likely familiar to many of you, some might not be -- but by placing Shakespeare alongside these canonical great writers, Jonson is reaching upward, rather than making an uncontroversial assertion. Jonson is making a conscious effort to situate Shakespeare alongside the influential literary greats as he and his contemporaries understood them, not simply describing the state of the English literary scene. Some of these particulars might reflect Jonson's own tastes and personal biases, but I don't think many people in 2018 would take issue with a commentator ranking Shakespeare alongside Spenser and Chaucer for influence in late medieval and Early Modern literature, or alongside Seneca and Aeschylus as landmark writers of tragedy in the Western canon. Kyd and Lyly haven't stood the test of time in the same way. (And to be frank this poem is the only context I ever hear much about Pacuvius and Accius -- they seem to function more as bywords for respectable Classical tragedy.) Some of these bywords for dramatic and poetic excellence are no longer bywords at all outside a specific context.
Shakespeare achieved financial success in his own lifetime and received some critical respect from his literary peers, but his works wouldn't be enshrined as classroom literature until much later. A lot has changed in 400 years, and in a modern high school classroom students might be reading other Early Modern dramatists' works but their primary familiarity will likely be with the works of Shakespeare -- in 2018 you're more likely to read Seneca's plays with an eye for parallels with Hamlet than you are to come to Hamlet as a complete blank slate well-versed only in Seneca. Who were the Shakespeares of Shakespeare's own day, in terms of commonly agreed-upon literary achievement in the English language, works you could discuss in a serious literary context as agreed-upon greats? Among others, Chaucer, Gower, Spenser, Sidney, and Drayton all get reliably name-dropped in the early 17th century with respect to their achievement as English-language poets. Latin-language drama and verse had a more prominent place in the schools and universities, and it would be fully possible for an educated commentator to discuss commonly-agreed-upon excellence in comedy and tragedy without once mentioning a playwright whose native language was Modern English. The big names of Classical poetry (the works of Ovid, Virgil, etc.) far outstripped any one English-language writer for lasting influence on Early Modern English literature, to the point where allusions and imitations of Classical writers are almost as ubiquitous as allusions to Christian scripture.
Shakespeare's works were wildly popular in their own time and beyond, but Shakespeare's contemporaries didn't rate him as one-of-a-kind in terms of earning power in the theater or as artistically one-of-a-kind -- his works were referenced, parodied, remixed, altered, and rewritten even in his own day, rather than being treated as a finished literary product beyond reproach or alteration. Shakespeare's legacy outstripped that of some other playwrights who in his own lifetime would have been considered his artistic and commercial competitors, but still not to the extent that other playwrights were completely overshadowed. The place in the Western literary canon we now associate with Shakespeare -- the greatest poet of all time, the one writer everyone will read in school, the one writer everyone can quote or allude to and have their meaning be universally understood -- was not achieved until the 18th and 19th centuries.There have been a couple good answers related to this aspect of the topic that might be relevant to your interests:
'Why is Shakespeare considered to be one of the best writers of all time? Has he always been taught about? If not, when and why did he become a staple of high school curriculum?' with answers by /u/OwlOfDerision and /u/Sunagainstgold
'When did William Shakespeare become "The best playwright ever"?' with answers by /u/Sunagainstgold