The value of the 1923 dollar coin is mostly derived from its 90% silver content. The 10% copper content is hardly worth the cost of extraction. These coins are collected for their numismatic value and whilst silver remains below $20 an ounce, it remains the case that they are worth more in their unmelted state.
By 1896 the Morgan silver dollar had been around for around 20 years and was an everyday part of American life. Transactions were carried out day after day with it. Nobody gave the fact they used a real silver coin a second thought.