I've never understood why JUST A MINUTE hasn't been adopted for a US version(aside from the 1954 DuMont version ONE MINUTE PLEASE). That show is one of the funniest programs I've ever heard.
Those with a greater familiarity can answer this, but haven't the British spent over forty years trying to adapt Just A Minute to television without much success? That would be a red flag, especially given that, as far as the US goes, I'm not sure that radio is an option.
ISTR that the first attempt at TV was within the last 20 years or so and TV producers have tended to monkey around with the format.
I'll admit that there isn't really anything about JAM that requires visuals, but I'd say that the same thing applies to basically all talk shows and a lot of game shows--you could cover up the screen and not really lose anything. If the BBC called me up today and asked for my advice for a new TV version, I'd say to get people with a background in performing and not just wits, and arrange the staging so that the person with control of the subject is standing at center stage with a little bit of room to move around, rather than keeping everyone behind a desk the whole time.