Why aren't nucleic acids on Nutrition labels?
This FAO report can tell you all about food analysis and why things are and aren't on the label: http://www.fao.org/docrep/006/y5022e/y5022e03.htm#TopOfPage


  First, not all nitrogen in foods is found in proteins: it is also contained in variable quantities of other compounds, such as free amino acids, nucleotides, creatine and choline, where it is referred to as non-protein nitrogen (NPN). Only a small part of NPN is available for the synthesis of (non-essential) amino acids. 


The DNA in food would contribute to the nitrogen content. Then (using a food-specific "Jones" factor) total nitrogen content is converted to protein content. So in a way it's already there. 

Listing DNA separately would require extra testing, and also the difference in daily use would be negligible. There's not that much DNA in food anyway and, like protein, DNA can be converted into new protein and energy. The Jones factor already accounts for this.