I think the reason, is paper money is worthless. In the old days, what you had in your hand had intrinsic value. If you had a 20 dollar coin, the coin had 20 dollars worth of gold in it.
The best way to get a very Christian country to feel safe with paper money that has no intrinsic value, is to say “in god we trust” on it.
Today it’s meaningless. I don’t care either way if it fell off or stayed on the next design.