Why is a silver dollar from Carson City worth more?

That statement is true for most but not all dates, 1870 being a major exception.

Carson City was a small mint established to produce coins near the mines, so that raw bullion didn't have to be transported long distances. Its size meant that it produced far fewer coins than larger mints such as Philadelphia or San Francisco, so its coins are usually rarer. In addition they carry a certain romantic "cachet" due to the mint's location in frontier territory and the history of silver mining in Nevada - see for example the Comstock Lode.