This post is so basackwards that I'm starting to think you're in the MSM.
JG was traded out of NE because TB12 didn't want him there. He's been the consummate team mate everywhere he's been. Great locker room guy. Unselfish. Teammates love him. He's exactly the type of person who would be willing and able to mentor a young QB.
TB12, Favre, Rodgers' are the type to not mentor young QBs, and never did so when they had the opportunity.
I would be very happy if the Texans signed JG to a Geno Smith type contract. I would front load it, include lots of playing time incentives, and draft a QB early in the first round. I would consider trading back, but not so far back that I miss the QB of my choice.