Nail on the head of what i was trying to get at (in the bold)
Even in evolution and genetics there's layering, building upon the foundation of the last change. In the case of monkeys typing, there's no foundation to randomly build up to shakespeare so it won't converge to that at any amount of time.
I'm not too familiar with the library version of this analogy, but my thoughts kind of diverge. Monkeys would have no conscious motive to jamming keys or a predisposed bias to create anything such as shakespeare, as opposed to infinitely typing essays about their love for bananas and nothing else.
But an infinite library of finite possible letters would have to converge to shakespeare at some point, where the monkeys them selves would break the finite'ness of what they can create by themselves being a none random entity... So in that case, yeah.
I think the two cases are fundamentally different tho. Living beings don't operate on the same randomness of inanimate objects, such as particles, stars, and other massive objects in the universe.... or in this case random letters.