To be honest, it's inaccessibility into the US market is probably preventing an American version with some outrageously characterized question master, which only offers essentially the same questions as this on.
In America we tried "Tough Crowd with Colin Quinn"; look how that turned out.
I can't even imagine whom we could cast as an American Stephen Fry or an Alan Davies. And the closest thing we've got to Brian Blessed is Joe Don Baker. It's just not meant to be.
John Hodgman has offered to do it, and Stephen Fry has given his blessing.
The reason it won't be shown in the US is remarkably mundane: too many music cues. The BBC has special music rights privileges that other networks don't, that have been in place for 50 years, so they can do anything they like with music.
I think that a gif of Alan swinging the phonebooks around must have been created by the time this finished airing. It's extremely fun to watch and would make a fantastic loop.