Why does iodine get oxidized to iodic acid and not periodic acid by nitric acid?
Nitric acid is not strongly oxidizing enough to get iodine to +7.  Relativistic effects tend to make the $s$ subshell valence electrons more stable than the others in heavy atoms (http://www.annualreviews.org/doi/abs/10.1146/annurev-physchem-032511-143755), so to some extent iodine acts as if it has only five valence electrons.  To pull out those last two electrons and get periodic acid, electrochemical oxidation is commonly used with a very high oxidation potential (https://en.wikipedia.org/wiki/Periodic_acid).