I know a lot here don't think the Sox will leave Chicago due to market size, history, etc. etc. however I wouldn't write it off.
The southeast is absolutely booming in terms of population growth and Illinois is ranked 47th/48th (depending what source you look at) out of 50 in growth and is actually currently losing residents.
Over the next 35 years Tennessee is expected to have a 27.5% increase in population vs. Illinois 3.6%. Nashville itself is expected to grow 56.1% by 2060.
Anyone investing billions on purchasing a team is definitely going to factor in future population trends to their decision.
Obviously it's anecdotal but I moved to NC a year and a half ago. 1 year in Raleigh and now near Charlotte. The first thing I noticed was how much new construction is going up. It actually blew my mind. Nothing like IL/Chicago area.