if you had infinite monkeys with infinite keyboards, they would all need to first read and memorise every work of fiction, as well as learn proper use of a keyboard, computer and the word processor of your choice. you'd also have to teach them proper grammar and syntax, as well as to read. given the commonality of grammatical and spelling mistakes by humans, this would be a near impossible task, as monkey childhood is too short to develop a brain close to ours, and reading a lot of texts, tweets and forum posts you can see that not every human can do that. not to mention the cost of not only the keyboards, but towers, mice and monitors and power. if you use the original typewriter (the phrase is basically 1000 monkeys+1000 typewriters=complete works of Shakespeare) then you need paper and ink, not to mention maintenance because typewriters are shit. plus, if Shakespeare alone requires 1000 monkeys, then think about all the other playwrights, and film adaptations, shorthand versions, Cliff notes and technically school notebooks and essays. you'd need infinite space to store all this, and a beast of a cooling system. monkeys would also fall victim to primal urges and nature, so you'd need cleaners to get rid of infinite amounts of monkey-shit and keep the babies out of there. then of course PETA would picket you for this.
So we come to the conclusion: why not let the machines do it.