It’s infinite monkeys over infinite time. Yeah, some would get carpel tunnel (an infinite number of them) and some would form labour unions (an infinite number of labour unions). There would be an infinite number of cults, and an infinite number of supreme leaders would rise. You’d have an infinite number of “it’s almost Shakespeare but you got one character wrong”, many more than complete Shakespeare works. And it would increase as you include more and more errors.

With an infinite amount of monkeys, this would start happening in the minimum amount of time it takes for any of that to happen. You don’t even really need infinite time once you have infinite monkeys, but finite monkeys with infinite time are different because then you have a finite number of outcomes and extinction might arrive before they have a chance to achieve each one.