Why didn't Light use Shinigami eyes? Why didn't Light Yagami use the Shinigami eyes? Couldn't it have been an easy task for him? Was it his arrogance and overconfidence? 

Alternatively, was he not willing to sacrifice half his lifespan, thinking it would be a loss for him?

Wouldn't it have been a wiser step to choose the Shinigami eyes and make life easier than playing and risking around his life?
From the Death Note Wikia:


  Ryuk offers to make a deal with Light for the “Shinigami Eyes.” Light refuses the deal, stating that he needs to live in order to rule over his utopian world. He asks Ryuk if there is anything else that he should know about the Death Note, and Ryuk says probably not.