Nominal Face Value

Special coins are often issued by governments for the purpose of providing something of value to collectors. One example is the American Silver Eagle, which is the official silver bullion of the US. The reverse of the coin, shown below, bears the nominal face value of One Dollar, even though the coin is composed of 99.9% Fine Silver which is currently valued on the "spot market" at USD $16.59 on SilverPrice.org


Another example is the Centenario coin issued by Mexico recently shared by @silversaver888. Her post states that it: "...contains 37.5 grams (1.2057 oz) of gold in an alloy of 90% gold and 10% copper" and the current price of gold is USD $1,460.31 on GoldPrice.org. Yet, the Centenario bears the nonminal face value of only 50 Pesos.

My question for my fellow Silver–Gold aficionados is: WHY?

What is the purpose of having a nominal face value that is so far below the actual precious-metals content of the coin? And if such coins are intended for collectors and not circulation, why even have a face value at all...?

I did a search of the Internet prior to asking this, but could not find a definitive answer from any credible source. THANKS for any insight that might be provided by those who understand such things!