For some background, I suggest you have a look a this:
A Matter of Balance
There's other papers around on the subject, as you can imagine.
One executive summary point is that since bridge balance is a ratio thing, if you have a low input impedance ADC then in absolute terms its CMRR is more susceptible to degrading because of source imbalance than if the input impedance was higher. For example, a 1 Ohm imbalance of the source impedances is minor if the ADC input impedance is 1 Meg. If the ADC input impedance is 2K, that same 1 Ohm imbalance is relatively much higher.
A proper instrumentation amplifier with high CMRR in front of the ADC certainly helps. You could build your own or buy something that may offer other features, too. For example, Jan Didden's AutoRanger works really well with a Cosmos ADC. The plot I posted earlier was made with one of those in the system. But, AutoRangers are no longer made as far as I know. E1DA has a Cosmos Scaler available now that is similar and works well. There are other tricks around this problem, too.
Another point is that a lot of DACs don't work as well into 2K input impedance as they might into 10K or higher. So, the distortion or the noise might go up because of the load they're trying to drive. Especially the distortion.
I'm going to stay on this soapbox for a moment and say that most actual home audio system components don't have great CMRR at their inputs. They're definitely not as good as Audio Precision test systems in that regard. (!) So, although the AP systems do exactly what they claim and do a magnificent job of providing an ideal environment for testing gear, that isn't really representative entirely of how the device under test will get used. This is one of the limitations of most testing. You can test the gear under idealized conditions or you can test it under real world conditions. Those real worlds conditions vary all over the map, which makes it that much harder. Think of it like Formula 1 race cars. They do tons of testing in various labs and wind tunnels. Extreme amounts. Then, they put the cars on the track. Things change then.
Yeah, if every piece of audio gear was immune to its use environment, these challenges wouldn't be a thing. But, not too many people are willing to pay for the added circuitry and other stuff needed to make preamps and the rest impervious to source imbalances, for example. For one thing, they'd need true differential inputs and very high PSRR. Balanced inputs and outputs would helping that, too. None of those come for free. Plus, imagine the hurdles a manufacturer would have to overcome to convince people of the value of the higher priced solution. Higher priced not only for their products, but the solution may well require people to change cabling to something balanced, too. People already are skeptical about cabling, aren't they? (Rhetorical question...)
In a sense, this is why subjective testing is valuable. The gear is tested under actual system use. Of course, the opposite side of that is that the subjective observations may only be relevant for that one system combination. If that.
This all isn't so easy after all. But, then again, maybe it's all good enough for most people. (Most being anywhere between 90 and 99.99999% of the people. That's a different debate that I'm not qualified to talk about, so I won't.)
