In researching some other stuff in relation to the 74HC165 I found a use for the 4th buffer in the 74HC125.
It's a tri-state device so the 4th buffer can be used to put the MOSI (on the 74HC595/TPIC6x595 for outputs) or MISO (on the 74HC165 for switch inputs) in high impedance mode so the SPI bus can be shared with other 'real' SPI devices that have inbuilt tri state capability via their CS/SS pins. The use of the tri-state buffer in this way requires a pin on the MCU to pull the output enable pin low on the buffer.