Carius method for quantitative analysis of halogens
1) $\ce{HNO3}$ is a more oxidizing acid than $\ce{H2SO4}$.  

2) The silver nitrate would not dissolve well in the organic solution.

3) Sulfide is an example of something you might worry about interfering as it forms a very insoluble compound with silver. But silver sulfide and most anything else that might interfere will decompose in the fuming nitric acid.