I was thinking the same but I think they wanted to go with a much younger generation of kages this time around. And leave Kitsuchi as one of the strong shinobi of the village
Only four possibilities:
1. He was the 4th Tsuchikage, before his daughter, Kurotsuchi became the 5th Tsuchikage.
Or
2. He died at some point after the war.
Or
3. He became a rogue shinobi.
Or
4. He didn't want to be Tsuchikage.