Billy probably assumes he has nothing to lose by going to trial. If he accepts a plea agreement, he gets LWOP; if he goes to trial and is found guilty, the most he'll get is LWOP. He's probably convinced himself that he has a chance of being found guilty of lesser charges, with the possibility of a reduced sentence.
He probably gets some satisfaction from making the state work hard and spend money while he fights for acquittal. He's probably dumb enough to think he could get acquittal.
Billy also grew up with a sense of entitlement, being a Wagner. He believes he's above the law and smarter than everyone else.
