Very interesting. My understanding is that even when the KJV was being written these pronouns were becoming archaic. If it wasn't for the Bible and Shakespeare I wonder how many English speakers would recognise them.
When the KJV uses thou or you (it uses both depending on plural vs singular pronoun references), that is because the underlying text is implying something different. Translations without this distinction are losing some of their meaning.
You = plural second person
It uses them because there is an actual difference. In modern English, you cannot tell if "you" is referring to one individual or a group without examining the surrounding context and adding your own judgement (a translator looking at the original text will have much better judgement).