I think he was praying that the People would tolerate a government.
They had recently had revolution to get rid of one, and I think such a prayer might be reasonable.
Of course, today we have a well-established government with many very comfortable on the teat. Such a phrase rubs us the wrong way.
At least, that is my take on it. :)
When referring to the “Separation” issue, you must remember what the Founders had just escaped.
In England, the Government and the Church of England are intertwined. The British Monarch IS the Head of their Church.
The Founders wanted no part of this concept in their new country and took steps to prevent it by preventing the government from establishing a religious body.
More people should know history.