Yes, I have to say an American style writers room would be a great idea. In fact I'd say series 1 of New Who was the closest it came, with a lot of back and forthing between the writers and the production staff (plus a lot of them knew each other personally), which resulted in a very sharp, consistent and focused thirteen episodes, especially when it came to characterisation. Even the bad stories had something to offer.
For that same reason though, I do wonder if it may not be viable. Even since series 1 (which had a two year production), I got the distinct feeling everyone was rushed off their feet.
Hence why, to me atleast, series 2's production felt amaturish compared to series 1. No one seemed to have a clue what to do with Tennant's Doctor and Rose seemed to be a complete blank of a character compared to what she was like in series 1. Moffat for example didn't realise that when Mickey joined the TARDIS crew, Rose wasn't exactly pleased, instead writing her as being fine with it. Nothing to do with writing, but a lot of the CGI had to be remade from scratch also (hence why the cgi Daleks looked cheap and nasty, vs the ones in series one). Similar problems continued and seemed to get worse with the shift to filming for HD.
Basically everyone is rushed off their feet trying to get Doctor Who out in a year. A writers room may end up fixing the writing issues... Or it could exacerbate the situation.
All in all though, I'm totally for it. It just makes so much more logical sense than what they do now.