I mean, in the Stabler seasons, they could go outside of the squad room, they could go to China Town like they did in Season 6 (https://en.wikipedia.org/wiki/Law_%26_Order:_Special_Victims_Unit_(season_6)) with Huang. They even had rape exam rooms scenes. They were also very diverse when it came to their victims.

Is it because Mariska Hargitay is being paid more and more per season, as is likely the rest of the cast? This would mean decreasing room in the budget for other set pieces and such.

For the latest season, they didn't even bother introducing a new character for the ADA role so they must have just made Carisi an ADA to save budget.