Why is copper (II) oxide used in quantitative analysis of carbon? What is the significance of using cupric oxide in the quantitative analysis of carbon? 

As far as I can tell from my research, only $\ce{CuO}$ is used to oxidize carbon to $\ce{CO2}$. Why can't we use other oxidants like $\ce{HNO3}$ or other metal oxides such as hematite? Is the use of $\ce{CuO}$ prevalent because of low cost or does it has some other special property?
You got the crux of it: low cost.  And it works, regardless of what the starting compound was.  And it's not just low cost to purchase, it is easy to regenerate the used cupric oxide multiple times by heating it under oxygen.