Since you brought it up, Jerry may have kept Landry if Bum Bright didn't make firing Landry a condition of the purchase. We will never know, of course. We do know Bum hated Landry bc he felt Landry snubbed him at some kind of social function. He tried to get Tex Schamm to fire him, but he refused.
When Jerry bought the team, he had no designs on running the football operations. That's why he was willing to hand that job over to Jimmy. The egomaniacal loser that we know as "GM Jerry" didn't surface until after Jimmy turned the team around. Jerry made the error of thinking that the person who approves an idea is on equal intellectual footing as the person who thought it up. Jerry thought he was an equal partner in the building of those super bowl teams b/c he got to nod his head and write the checks. Its a tough thing for a man of jerry's immense ego to admit and he will likely take his pride to the grave.