As a child, I was taught that to show reverence and respect, the words thee and thou should be used in prayer, rather than you and yours. I accepted this and it has become my comfortable language of prayer.
It came as a sweet revelation to me when a few years ago I learned the proper usage of thee and thou. Contrary to the now widespread belief that thee and thou are stuffy and formal, the opposite is actually true. When those words were in the common vernacular, you and yours were also used. However, thee and thou were for addressing those closest to us, you and yours for stuffy, formal occasions and when speaking to those whom with you did not have an intimate relationship. In one of our family's favorite books set in the Appalachian mountains during the great depression, Grandpa properly expresses his love for Grandma with the words, "I kin ye, Bonnie Bee."
This past week, much of the world focused on England and we twice heard the words, "I pledge thee my troth." Of course the word thee was used. To say "I pledge you my troth" would imply that I'm marrying you, but I have no deeply held feeling for you and don't know you that well.
If Heavenly Father were an "unknown God", you and your would be sufficient. I think it's a beautiful thing that as we use the language of prayer, we are acknowledging and confirming our intimate relationship Him.