The value of a DDC is much more than just converting to I2S. It does several things depending on the product, since I have a Denafrips DDC I'll speak there.
Convert the input signal to I2S (used internally in DACs/streamers/etc), galvanically and optically isolates the signal to eliminate noise and jitter, re-clocks the signal using the DDCs crystal oscillator.
Prior to the 15th versions, the Denafrips Ares and Pontus DACs use high quality FEMTO clocks, the Venus used a TXCO (temperature compensated crystal oscillator), and the Terminator II and Terminator Plus used OCXO (oven controlled crystal oscillators).
After the 15th, the Ares and Pontus use a LPNO (Low Phase Noise Oscillator), the Venus uses OCXO, and the Terminator 15th uses dual OCXOs, and I have no idea what a Terminator Plus 15th would be when it is released (if it is needed)
SNS
As you pointed out, you do need to be careful when adding a DDC to a DAC. You never want to downgrade the clock, so you want the clock in the DDC to be as good or better than the clock in the DAC.....in almost all cases, the clock in the DDC takes preference over the clock in the DAC
