I disagree that "I'll" mimics speech. "I'll" and "I will" are two different ways of either saying or writing the same thing. In the beginning middle of a sentence, they're generally interchangeable: "I will go to the store." "I'll go to the store." "If you're going to be that way about it, I will go to the store." "If you're going to be that way about it, I'll go to the store." There are some nuances where "I will" is the more likely or only possible version. When expressing firm intent, when ending the sentence, when it's the whole sentence: "Don't eat the fries." "I will eat the fries." "I told you not to eat the fries!" "Too bad." Here, "I'll eat the fries" is possible, but it slightly changes the meaning of the sentence. "Will you walk the dog later?" "I will." Here, "I'll" is not an option." "I know you. You won't walk the dog." "I will walk the dog!" Here, again, "I'll walk the dog" is possible, but it slightly changes the meaning. "You will too." "I will not." Here, "I'll not" would be grammatically correct, I think, but it would sound archaic.
Just pointing out that, technically, if "I will" is the whole sentence, it is also ending the sentence.