The real reason there was a shortage of coinage in Civil War times and years after was that US Notes were made non-convertible and the public preferred gold, silver, and even copper coins to the worthless paper. The Fractional Currency was usable at the post office for stamps, and several issues pictured stamps of the era. Many issues had no perforations (as stamps do) and were issued as sheets since the perforating machines couldn't keep up with the printing presses. There were few paper cutters in the average citizens' hands in those days, and most were cut apart with scissors, making for lots of odd shaped and sized notes in circulation.

Gresham's Law observes that "bad money drives out good", again evidenced in the 20th century when the public kept their silver coins and spent their US paper money.

Remember that 25c was not chicken feed in the 1860's, being worth as much as $5-10 measured in today's non-convertible paper money.