Many years ago I hitched a lift with the playwright Terence Frisby. Naturally as I was an English Lit student, we started talking about plays and how someone became successful as a playwright.

He explained to me that if you want to write plays, you've got to act. theres no other way. you tread the boards , you see what actors are capable of, what works, what doesn't work, you do it for years - everything else you can fake. You can write about kings , emperors, miners, gangsters, anything - but you have to have a firm grasp of what keeps the audience from dropping off to sleep.

could be you are underestimating how long Shakespeare had to work at his craft - and overestimating how much he had to know about history, poetry etc