Also because I don't think they could afford to pay what they paid Jones AND pay Barkley what he's worth.
If Jones had been a second-round pick who impressed as a relatively unheralded QB who won the job from Eli Manning and had glimpses of good play, the pressure on him would be so much less. But they used a very high draft pick on him, and now they've sunk a lot of their salary cap into him, so the knives are going to be out.
Playing-wise, his natural career arc at this point would be to settle in as a backup like Andy Dalton, Mitch Trubisky, Joe Flacco, Jimmy Garoppolo or Carson Wentz. But I'd have to think the cap hit would make it impossible for the Giants to move him.