The NCAA Tournament might have played a part in the ratings drop but I think people still would've passed on the show had those episodes aired in the fall.
I don't know or think Aaron Rodgers will succeed Alex, but he might be among the top two IMO. He is one of the top names in his position and within the NFL (current period). He puts in the hard work, pays attention to detail, and when you think he's done, he isn't. The man continues to evolve, and one would imagine that he's one of the best based off of skill set and off the field dedication.
While several people may or may not have what it takes to host full time, Aaron's preparation for hosting Jeopardy is one that I admire a lot. You really don't get a lot of people within the gameshow industry paying attention to certain things or acts within the show they are running. It might seem unimportant, but I think it's pretty important to learn and adapt to every little thing that took place in the past.
That's just my opinion; I think Rodgers should be himself & I don't think he should or can emulate Trebek that much. It is just nice to see him put in the work as if he really wants to be the next person to star on the show as a host