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.
These pronouns were adopted by groups like the Quakers for a long time after the KJV was made. they didn't refer to a single person with "you" because it is a kind of "royal we" where you ascribe plurality to a singular person (when they believed that only applied to God).
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.
It's, for lack of a better term, "High English." It is meant to sound grand, and thus the grander old style was used. Which is entirely appropriate; IIRC the original Hebrew uses grander language for poetic passages & the words of the LORD.
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).