Having watched the original "Jeopardy!" during the early 1970s on NBC, I still consider Alex the "new" host of the show, as I do Pat Sajak on Wheel, even though he's been hosting since 1981!!! Alex definitely is synonymous with Jeopardy!, and I remember when it first came back in 1984, many fans of the old Jeopardy! had to get used to this change, but they did. I think the fact that the old Jeopardy hadn't aired since 1979 on NBC, and there was a 5 year "hiatus" for the game helped somewhat. We talk of Price is Right being in its 40th season, Jeopardy has been on TV now for 43 of the past 48 years on TV, only having a hiatus from 1979-1984.
One person who was not mentioned as a possible successor to Alex is Bryant Gumbel, the former Today show host. He kind of reminds me a bit of Trebek in some ways. He has that air of "superiority" about him while at the same time it seems Bryant might be able to "kid" with a Jeopardy contestant.
I think finding a successor for Alex could prove far more difficult than for Pat Sajak. Comparatively speaking, the Wheel of Fortune host has a far easier time of it. Trebek & Fleming both became master craftsmen in the fine art of hosting Jeopardy! So many pronunciations, and a lot of talking, and rapid fire pace type questions. They made it almost look effortless, but I know it is anything but that!
I think while on the subject, there's also the thought of finding a successor for Johnny Gilbert. He sounds as fresh as ever to me, but he is 87 years young now. I would suspect if and when Alex eventually steps down, and assuming Johnny is still able to announce, that they might step down together. Any ideas about who could succeed Johnny? At best the show will find successors, not replacements...