As mentioned, Soldier Field is visually a beautiful location. What is it that makes it a terrible location? Logistics? I've been there but don't remember any really bad traffic as we got there early and stayed late tailgating. Do they have a dedicated subway stop? If not and they could add it, would that do it? I know they've always had issues with the grass because it is managed by the city instead of the club.
I lived just west of Soldier Field for 8 years.
There's a Metra (train) station very close to the Stadium, but it only serves the southern suburbs. The closest L is the Roosevelt station about 1 mile away. Traffic generally sucks more on gameday, that's for sure. Going to/from north or west to/from the stadium necessitates going through the Loop one way or another which is...yeah...slow on a good day with multiple bottlenecks.
Parking is relatively limited directly around the stadium and the adjoining neighborhoods are very dense. There simply isn't a lot of space to park and walk.
The Bears have two things they really want.
First, the Bears want to own their own stadium, as most NFL teams do. By owning the stadium, they can generate additional revenue on non-game days. The City of Chicago Parks Dept owns Soldier Field, so the revenue from any non-Bears events go to their coffers, not the Bears.
Second, the Bears want to be able to develop the area around their stadium like SoFi in LA or Jerryworld. This is another huge potential revenue stream for the team from hotels, bars, shops, other venues, etc.
Soldier Field is owned by the city and is situated in a park. Long-standing city laws and traditions prohibit development on the lakefront, basically anything east of Lakeshore Drive. On the rare occasion the City wants to cross that line, there are tons of citizen groups that will fight it tooth and nail to the death. George Lucas basically wanted to give the city a museum about 8 years ago, but only if he could build it just south of Soldier Field. It eventually got shut down - there were other issues, but the city ultimately said no to that location and he wouldn't accept an alternative.