That is a very extreme interpretation of our Constitution that has only been adapted recently. It is being used ban public display of religious expression that has any connection with Government. And now that government consumes about 40% of the GDP, that adds up to a huge ban. Not establishing a religion and not showing any favoritism are two different things in my book.
If the Founding Fathers wanted the government to be able to show favoritism, they could well have done so.
The Constitution enumerates and limits the powers of the government. Nowhere does it give the the government the power to prefer one faith over another. You can say my interpretation is "modern," but you can't change that fact.
Why do you suppose the Founders didn't give any indication that the government has the power to endorse a religion, as you claim?