Yeah, it makes way more sense if you take the view that Judas was Jesus' most trusted disciple and was specifically entrusted with the task by Jesus Himself, as the Gospel of Judas and other sources say.
TBH it's not so much like that. GoJ's Judas is the pawn of that being who created and rules the material world - nope, not God, some angel named Nebro/Saklas. Said being who obviously doesn't want Jesus (sent by that other, higher God) to complete his task; Judas is the tool that will ensure Jesus leaves his bodily shell to prevent him from completing his mission of revealing that other God to humanity. But that's it - all Judas will hand over is that bodily shell. The 'real' Jesus will escape, because
So it's not so much 'You gotta betray me' as 'You'll betray me, right? Eh, sure go ahead if you dare'.