I would suggest that the only way to answer a subjective question is with subjective impressions. To try to provide a theoretical answer to a subjective question is fraught with difficulty.
In trying to arrive at a theoretical answer you then start with two fairly bold assertions and I disagree with both of them.
I suspect that the basis of our disagreement is that you seem to view DACs as “digital” devices, i.e. devices working with mathematical manipulations of ones and zeros. DACs are electronic devices, in reality they work with voltages and currents which are entirely analog phenomena. The “digital” parts of the circuit process voltages that are in fact codifying ones and zeros but while they are “digital” in the logical domain, in the real world they are still very analog.
So while some of your logic holds true in the “digital” domain (the mathematical result of performing a filter function on a dataset will always be the same on paper) this is simply not how things work in reality. Rise times are not instantaneous, linearity not perfect etc.
Add to that the fact that many parts of a DAC are not “digital” at all, i.e. they don’t even process symbolic ones and zeros (power supply, output stage etc.) and it becomes clear there is actually no difference between a DAC and any other piece of audio electronics like an amp. While some might argue that all “well designed” (by which they often mean “in theory and abstracting away all imperfect real-world behaviour”) examples “should” all sound the same, in fact they all sound different.
And since DAC chips are not pin-compatible (unlike for instance op amps) it is not really feasible to build a test harness that eliminates all other variables in order to easily compare them. So in practice you are comparing whole systems or at least subsystems, where there are many more variables.