Number 1: Wow, I am SHOCKED that this is a new game. I had no idea this show was still relevant. Number 2: Who the heck is this clown? THQ couldn't be bothered to get Jeff Foxworthy's likeness?

Sorry, I don't watch Jeopardy

Contracting Foxworthy for a low-budget title probably wasn't worth it. Probably wasn't even considered for more than a few minutes given a popular personality like him doesn't get out of bed for less than a $100k (per scheduled event).

Why do you assume he might have been interested in loaning his likeness to a videogame?

Or - as Cologno has pointed out already - why do you assume, he might have been cheap enough for a game whose production probably had to ran on a rather tight budget?
(Half-)prominent likenesses aren't available for free.

And while we're at it: why not ask John Cena?
He was the last to host the show in the US.

Apart from that: Foxworthy would only appeal to a fraction of the possible audiences (= the US Americans).
The show got sold to 55 countries, each of which featured their own host(s).