My first DDC was the Hermes. I tried it on a whim, did not perceive a sonic improvement, and eventually sold it. After going a year without using a DDC, I changed some things in my system, added a Sonore Signature Rendu SE optical streamer which only has a USB output, and decided to try another DDC, mostly to have additional connection options.
I am now using a Singxer SU-6 connected to my Sig Rendu SE streamer by a short USB cable and am currently running three different DACs connected to it by AES/EBU, S/PDIF, and toslink/optical. In each case, I do not discern any loss of performance by having the DDC in the path. Using the DDC is also a great way to compare different inputs going into the same DAC since you can literally have them all connected at the same time. The SU-6 has operated without a glitch in the 6 months or so since I have owned it.
I believe you are correct about inputs being "component dependent." None of the DACs currently in my main system have an I2S connection but I previously used I2S with Metrum’s Pavane and Adagio DACs. I didn’t hear much if any difference between I2S and the other digital inputs. I suspect the most significant sonic difference would occur between using a USB input, where the DAC’s clock does the work, and S/PDIF or AES/EBU inputs.
As discussed in the linked Singxer SU-6 review, there are likely jitter improvements associated with using a DDC, but whether those will be audible will probably depend on your system.