and why not choose a former game show host?? Would the fans hate them???
The problem I can see is that
Jeopardy! is a format from the 1960s that was revived in the 1980s, and functions like a game show of that era—that is, there are enough actual game mechanics going on to fill the whole episode, and the host's job is to facilitate the contestants' interactions with the game mechanics. The only fluff not having to do with the game is the contestant interviews at the start of Act 2.
Contrast this with the modern, post
Who Wants To Be a Millionaire? style of game show, where you have about one fourth of the episode doing actual gameplay and the rest sitting around a dramatically-lit set trying to build tense moments. A host of that era of game show would do pretty poorly with
Jeopardy!, because they require vastly different skill sets, so you'd basically be having to train someone from the ground up anyway. At that point you might as well just go with someone with good diction and no game show experience, like LeVar Burton.
The only game show hosts with any relevant experience are dead, retired—Wink Martindale is an excellent example of the game show host archetype of this era but is 86 years old—or hosting one of the few legacy formats still on the air: Pat Sajak of course, Drew Carey, and Wayne Brady. I wouldn't consider
Family Feud adequate hosting experience for
Jeopardy! because, as it was originally created as a vehicle for Richard Dawson, it's one of the weakest of all the Goodson-Todman formats, and is far more host-dependent than
J! is.