Some DAC / ADCs might show rather large idle tones at DC. Some ADCs (don't know about DACs) do remove DC and thus won't work with DC at all. Many audio codecs also need a constant flow of data, even if constant values are wanted. Usually the gain and offset drift is not that good, but often still not very bad.
As audio usually is at least 2 channels one could use one ADC channel to monitor an external reference and thus way tie the data to an external reference even if the ADCs/DACs use an internal one only.
For the ADCs there are some alternative, relatively cheap ADCs (e.g. MCP39xx series) with reasonably DC specs.