I'm fascinated by this train of thought:
"Bears are moving out of the city. Fans will want a team in the city to follow."
"The Jaguars may move and become Chicago's second team."
"They should play in the Bears' stadium in Arlington Heights."
You missed one, "The Bears hold all of the cards, so it is they who will decide if the Chicagoland area, or let's just call it Chicago, ends up with another team and where that team will play. Seeing how the Chargers are stuck paying the Rams to play home games in the Rams stadium, the Bears may consider that to make even more money for themselves. If another team doesn't like it, they can find a home in another city."
Fans can go pound sand in the Bears mind. Fans will not have a say in what happens because they do not have a vote on whether another team comes to Chicago and where they would play if a new team would come. The McCaskeys do. What is best for the McCaskeys? Either the Bears remain the only team to play in Chicago (the Chicagoland area) or the McCaskeys get something for it which would be a renter (the Jags?) in their new stadium.
I could see the Bears financing the new stadium and Khan financing everything else that is to go in the new stadium area (housing, shopping and entertainment).
One thing that could happen is the Bears voting (allowing) the Jags to move to Chicago while Khan gives them an amazing financial deal to allow the Bears to comfortably build their new stadium.
Either way, no team will get to move to Chicago unless that team sweetens the pot for the Bears to want to make a deal.