Why are the heads on coins all side portraits, but the heads on paper money are front portraits?

The heads of former presidents appearing on (dollar) coins are all side portraits, Lincoln and Jefferson are on the cent coin, and Roosevelt, Washington and Kennedy are on the dime, all with side faces. But on paper money, you can't find the side. Washington on the 1 dollar bill, Lincoln on the $5 bill, Hamilton on the 10 bill, Jackson on the $20 bill, Grant on the $50 bill and Franklin on the 100 bill are all positive portraits. With a few exceptions, the situation in other countries is similar: coins have profile images and banknotes have front images. Simply put, although most painters prefer frontal portraits, technical problems in metal carving make it difficult for people to draw highly recognizable frontal portraits on coins. The space available for painting on coins is generally only 4 square centimeters. Because it is not fine enough, it is difficult to draw an easily recognizable frontal portrait. On the contrary, it is easier to identify the subject if only the side is drawn. It is technically possible to draw a detailed portrait on a coin, but the cost is extremely considerable. At the same time, with the circulation of coins, delicate details will soon be worn away. In that case, why throw it away on paper money? This is because the front portrait is fine and complicated, which can prevent counterfeiting.