“Why would anyone write an Othello or a Macbeth and then not publish them so they could get credit for them and people could read them?”
This is perhaps the most common question that I hear, and it is an excellent one. I typically respond that Shakespeare never published the majority of his plays either — including Othello and Macbeth. Instead, most of Shakespeare’s plays were printed and attributed to him after he died. Why? At that time, plays were mostly meant to be performed in the theater, and there was not much of a market for them to be printed. And this was particularly true in the early Elizabethan era when North wrote most of his plays.
In their introduction to Lost Plays in Shakespeare’s England, David McInnis and Matthew Steggle estimate that roughly 3,000 plays were staged in the commercial theaters between 1567 to 1642, and of that number, only 543, or a little more than 18%, survive. The main reason so many plays are now lost is not that they were published and then perished but that they were never published in the first place. But as low as this number is, it is inflated by the percentages of the first half of the seventeenth century, when plays became increasingly popular. If we focus just on the 1500s, the percentage of printed plays is lower. For example, the business records of the Elizabethan theater-manager Philip Henslowe show that only 30 of the 280 plays that he produced between the years 1592 to 1603—a shade over 10%—are extant. If we examine the decades that North mostly wrote—from the 1550s to 1580s—we find the percentage of printed plays was even lower.
And this is certainly understandable. The first truly successful public theater would not be built until 1576. Prior to that, plays were mostly a privileged diversion.
Noblemen, like the Earl of Leicester, funded the theater troupes, and they produced their plays before the Queen or at private manors, universities, or the Inns of Court. Naturally, publishers would have had little desire to produce scripts of plays about which the general public was largely ignorant. For example, Leicester’s theater troupe performed plays steadily for nearly 30 years (1559-88)—in London, in the suburbs, in tours to country estates and universities, even in Europe. Yet, as Terence Schoone-Jongen writes, “little information about Leicester’s repertory survives.” Who wrote all the plays that they were performing for those decades? Scholars have not even ventured a guess at the identity of any of their playwrights. But new-found records now confirm that North did indeed write plays for Leicester’s Men.
Another confounding factor is that many of those plays that were printed during the Shakespeare era were published anonymously. Thus, our knowledge of Elizabethan playwrights often derives not from published title-pages but from the work of literary archaeologists who, through historical research and linguistic analyses, have uncovered their identity and reconstructed their oeuvres. Thomas Kyd, author of The Spanish Tragedy (~1588), was mostly unknown to literary scholars for centuries after his death. Prior to that, few had ever come across his name or knew the authorship of his plays. As described in the classic 1911 Encyclopædia Britannica:
Kyd remained until the last decade of the 19th century in what appeared likely to be impenetrable obscurity. Even his name was forgotten until Thomas Hawkins about 1773 discovered it in connexion with The Spanish Tragedy in Thomas Heywood’s Apologie for Actors. But by the industry of English and German scholars a great deal of light has since been thrown on his life and writings.“Kyd, Thomas (1558-1594),” The Encyclopædia Britannica, 11th ed. (New York: The Encyclopædia Britannica Company, 1911), 15:958.
The early seventeenth century playwrights Thomas Middleton and Anthony Munday have similar stories. It is only through later scholars that the extent of their dramatic contributions has been realized. North is no different in this regard. He is just the latest playwright to be discovered and saved from obscurity through a posthumous reconstruction of his canon.
Most importantly, however, this point is entirely moot. The question is not really whether someone would write an early Hamlet, The Merchant of Venice, or Romeo and Juliet, et cetera, and then not publish them. We know that this necessarily happened. We have records of these earlier plays. We know they existed and that someone had to write them. The only question is: who?
 Neil Carson, A Companion to Henslowe’s Diary (Cambridge: Cambridge University Press, 1988), 82-84.
 Terence Schoone-Jongen, Shakespeare’s Companies: William Shakespeare’s Early Career and the Acting Companies, 1577-1594 (Burlington, VT: Ashgate Publishing, 2008), 175.
 In the early twenty-first century, a similar effort was made to reconstruct the canon of Thomas Middleton, who also had remained little-studied until the nineteenth century. Researchers had not been quite sure about the extent of his writings until the last few years, when stylistic analyses indicated that he had helped Shakespeare adapt both Measure for Measure and Macbeth. As Gary Taylor writes about the once forgotten playwright: “The first attempt to put him back together again was made by the Rev Alexander Dyce in 1840. Dyce’s edition immediately established Middleton as a major playwright, but it also attributed to him some mediocre work by other people, omitted some of his best work, and seriously distorted his biography…” See Gary Taylor, “The Orphan Playwright,” The Guardian Online, www.theguardian.com/books/2007/nov/17/classics.theatre (accessed 20 January 2020).
 Anthony Munday was another writer who had to be saved from anonymity by modern researchers. Quoting I. A. Shapiro: “If we may trust the scanty contemporary references to him, Anthony Mundy was one of the most prolific and successful of Elizabethan dramatists; in Francis Meres’s opinion he was also one of the best. Yet very few of his plays are known to be extant, and even those have been identified as his only in modern times.” See I. A. Shapiro, “Shakespeare and Mundy,” Shakespeare Survey 14 (1961): 25-33; 25.