In simple terms, a DAC's analog section is no more or less compromised than any preamp or amplifier circuitry, except for the presence of high-frequency analog filters. In contrast, the adverse signature of the digital domain and digital/analog converter sections, results from jitter, compromises in digital filtering, and characteristics inherent in the DAC chipset. If your DAC has treble glare, hard or flat treble and upper midrange, has a smeary non-resolving quality, sounds synthetic, or becomes fatiguing, you are most likely hearing weaknesses in the digital section and digital/analog conversion. To say that "the sonic character of its output is obviously the sonic character of its input" is just Benchmark marketspeak.
Finally, there are the inherent limitations of the RBCD medium itself. Sadly much RBCD mastering is done poorly and is over-compressed, leading to some of the above symptoms regardless of playback equipment. However, with the right front end, much RBCD can approach SACD and vinyl.
Fortune cookie say that until you get right with CDP or have a good vinyl front end to compare to your CDP, you will experience much restlessness and waste of time & money swapping downstream components.