Many people throughout the ages have complained that the loop of their amp, or the loop of their MFX alters the sound.
Conversion quality is one of the factors that can be at play, although it may be less important the better conversion gets. But absolutely a decade ago it was a factor, and two decades ago it was an undeniable factor.
Discriminating ears can hear the difference between them. You can argue that for a guitar signal chain it doesn't matter, but in a MFX, it is absolutely 100% important when listening to headphone outputs for silent practice. There is still a noticeable difference in quality between headphone amps. Conversion is one of the factors involved and having an absolutely silent noise floor is needed for the illusion that you are not wearing headphones.
I am not set up to measure the audio quality of my headphone output, but I can tell the difference in quality between different units. Just because most people can't prove it with sophisticated measurement, does not mean it isn't true.
Someone complained about the quality of the VP4 in his signal chain. I suggested someone run ten generations of loopback through it to see what it does, vs same loopback through a patch cable. I agree in testing and measurement, just don't have the ability to do it.