Yes, the Broncos should likely honor their contract with Malik Jackson and keep him. Unless he has done something terrible, or he is ready to move on, there is no reason to get rid of him. It's probably a good idea for the team officials to sit down with him and discuss options together.
No team wants to lose a player that they value. It makes sense that they would want to fight to keep their own guys. However, if the decision is made that he will not stay, the Broncos should accept that answer. While they should try to keep him, they still need to know when to let go.
The Broncos don't have the cap space Jacksonville does, and in a perfect world, he'd stay there. However, they can't match the money, and to do so for one player, even a good one, would hurt the team's overall financial picture. The Broncos are a pretty deep team, and they should be able to find some talent to replace Jackson.
The Broncos just won the Super bowl and have lost the centerpiece of their team. It will be a long while before they are rebuilt and ready to contend for a title again. Meanwhile, best not to spend money now that will be better used later. Malik may be a fabulous player, but he may not work for what the team chemistry will be in five years. He may not even be active by then.