Why do chromyl bromide and chromyl iodide not exist?
Chromyl Bromide does exist.  See Halogen Chemistry at page 246:  


  Deep violet needles of chromyl bromide are obtained by treating chromium(VI) oxide with $\ce{CF3COBr}$ and HBr in the presence of phosphorus pentoxide. A less pure sample is made by treating chromyl chloride with a large excess of hydrogen bromide. The compound, which is hygroscopic, is purified by vacuum distillation at —135° (Zellner, 1949; Krauss and Starke, 1962). 


The book continues:  


  Chromyl iodide has not been prepared and may not exist because of the powerful oxidizing property of the chromium (VI) oxidation state.  


See similarly The Chemistry Of Chromyl Compounds Chem. Rev., 1958, 58 (1), pp 1–61:  


  Chromyl bromide has likewise been isolated within the past few years (273,
  274). The modern work corrects earlier reports of the compound (77).  
  
  While there has been one report of the formation of chromyl iodide as a deep
  red liquid from a mixture of dichromate, iodide, and sulfuric acid (87), a majority of observers (77, 96, 128, 196, 255) deny this observation and the existence of the compound. There is little likelihood that the iodide can exist, in view of the large free-energy change attendant on the reaction:
  
  $\ce{2Cr^{+6} + I- -&gt; I^{+5} + 2Cr^{+3}}$