Articles 230-204 and 230-205 address Isolating Switches and Disconnecting Means.
Does a customer-owned 12 kV Overhead Service require a disconnect that simultaneously disconnects all ungrounded service conductors or can they use 3 individual fuses?

Looks like if it’s considered a “service disconnect,” then yes. 230-205(b). Disconnecting Means. Each service disconnect shall simultaneously disconnect all ungrounded service conductors that it controls…

Believe me, if you ever need to personally operate it, you may very well appreciate a gang-operated switch.