I wonder why they never minted a .75 cent piece.

They minted all those other denominations...Go figure.

What is money, in reality, but dirty pieces of paper and metal upon which privilege is stamped?
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Good question.
Great transactions with oih82w8, JasonGaming, Moose1913.
AND you muct remember for much of the first half of the 19th century, U.S. coins were a minority of what was used for money in the United States. The first U.S. mint did not have the capacity to issued enough coins for our economy. And many of the coins that it did issue did not circulate because of the flaws in the bi-metalic system. When the price of gold and silver fluctuated the coins that weighed too much disappeared from circulation. Therefore it did not make a lot of sense for the U.S. to take a radical path when it come to the denominations that it issued.
Might as well cover all possibilities
We have not had any currency or coins that were more than 50% in value of the next larger denomination in the last 110 years plus. The reason; the 2c, 3c, , 20c $3 denominations which all eventually failed due to lack of acceptance. The $4 stella was a pattern.
All the other comments by BillJones do apply as well.