We know from the season premiere that Constantine is actually being hunted by an otherworldly Big Bad of his own because of his past actions, and this entity is so scary that the Fairy Godmother the Legends caught chose to be sent to hell instead of forming an alliance with the man.
For that matter, someone who’s come to mean a lot to the team is Constantine.
Tripping through time to fight baddies is one thing, but when you come up against demons and such, it’s good to have a magic man on your side, and for the Legends that dude is everyone’s favorite supernatural detective.