CathInfo.com

And yet, all the English Bible translations from back then used "thou" and "thee". Similarly the Germans always used "du" for God. In Latin, Hebrew, etc. there's no distinction between formal and informal versions of the 2nd person singular. Most languages with a distinction use the informal version. A notable exception is French, but there's plenty of usage of "tu" for God even in French dating back centuries.
https://en.wikipedia.org/wiki/T%E2%80%93V_distinction
I'd also question the assumption that "thee" and "thou" are formal in modern English. They're just archaic. No one addresses a President or King or anyone as "thou"(it's Your Majesty, not Thy Majesty). People only do it with God because they're referencing old translations, which is perfectly fine of course, but to act as if saying the general "you"(which is used both formally and informally in modern English) is disrespectful when in fact "thou" and "thee" were brought in when they were informal, is just plain wrong.

It would be clearer to say that in the past "thou" was a familiar version, rather than an informal version.  It was used to show the closeness and intimacy of the our relationship with God.  At that time "you" was used with strangers, but it was not impolite or disrespectful to use "thou" with family and friends.

As Matthew said, however, the historical usage of these words is irrelevant. Now,"thou" is referred to as hieratic language, that is, a kind of formal language set apart for solemn and religious contexts.  It is not correct to call it archaic, since it is still in current use.  Nor is it "referencing old translations."

As we use it today, "thou" fosters a sense of the sacred because this is special language for God, while "you" is the everyday term.  I might not go as far as calling "you" disrespectful, but it is more appropriate to have special language.  Our worship is full of sacred things set apart for God.  The vestments are only for use in liturgy.  The Chalice is not used when one wants a drink of water.

We live in a culture greatly lacking in a sense of the sacred, so it makes sense that it is good to use words that foster it.