what is the purpose of the analog part in the DAC

Yes all DAC chips output analog signals but they're often not in the right format for sending to a preamp. For example many DAC chips output current rather than voltage so require an I/V (current-to-voltage) stage. Many DAC chips output balanced signals which need to be converted to single-ended. Then there's the question of ultrasonics which need to be removed. Finally there's buffering to drive a cable and potentially a poweramp. 

The "I/V stage" is an analog stage and it is required at a minimum. The job of the I/V stage is to take those DC pulses as an input and help to try to form that into an analog waveform.

This isn't accurate. Not all DAC chips need an I/V stage, only those whose internal circuits work in current mode. AKM chips (excluding the AK4499) work in voltage mode and use capacitors as DAC elements so they output a voltage directly but normally balanced.

The DC pulses out of a DAC are already analog in nature, that's the basic function of a D/A converter.