But to answer your question, I do not know why they stopped doing this. It's pretty uncommon nowadays for teams to play semi-home games in a larger city nearby.
The only school that I know of that still does this is Arkansas, and there has been some major pushback regarding them playing 1 game in Little Rock every year. In recent years, they've tried to play the worst opponent possible for the Little Rock game because they tend to play poorly there. Alcorn was the Little Rock game in 2016 and FAMU was the Little Rock game in 2017. Next year's game against Ole Miss is the last game on the LR contract. Quite possible that will be last Arkansas game ever at LR/WMS.
Louisiana Tech used to play regularly in Shreveport, with many of the games coming against P5 competition. They played Oklahoma State there in 2002, Miami in 2003, and Texas A&M in 2012 (last LT game at Independence Stadium). In the 90s, they played Baylor, Cal, and Texas A&M there. To this day, Mississippi State is the only P5 schools that has played in Ruston (Baylor is scheduled to make the trip in 2022) instead of Shreveport.
Alabama has not played at Legion Field since 2003. Auburn has not played there since 1991.
I wouldn't mind an occasional game in New Orleans or Jackson, but it needs to be against a program that people have heard of (not Charlotte or ODU). Our fans LOVE the six home games we have each year, so it would take some selling. New Orleans would be easier, because it's a fun city and the Superdome is still in pretty good shape. Jackson would take some selling, but I still think it's a good idea. Jackson is our state's largest metro area and we could definitely use more publicity there. VMS certainly isn't in peak condition, but it's not that bad. It's pretty comparable to Independence Stadium where we're playing in 2 weeks.
"We played 12 SEC games when I was here, and 14 of those were on the road!"
- PW Underwood (RIP)