To me, it seems perfectly understandable that you'd feel that way. Because he IS doing an accent, and for you in Britain, it's totally obvious that he's doing one because you've had a long history of watching Laurie on TV.
So maybe I was a bit critical to say his accent was poor, just that to me, hes still 'doing an accent' rather than allowing me to forget hes an actor in the first place.
Here in the US, although there are some people who were familiar with his work, most people were not. So when most people here first saw House, they weren't distracted by the "oh, he's doing an accent" thing. They just accepted that he was American, and he did the accent so well, that they could accept it without question. It's only when he started popping up on talk shows speaking in his natural voice or when articles started to be written about him here (in just about every major magazine and newspaper) that many people found out he is British. And even after that, when you'd expect people to then start nitpicking the accent, they didn't. I know that when I watch House, I don't even think about the fact that he's doing an accent. It just seems totally natural. But again, I can see why someone in Britain would have a harder time with it.
Just to make this post a bit more on topic. One thing I've found interesting in the new shows coming up is the cluster of shows with vampire "detectives" as leads. You've mentioned Moonlight and New Amsterdam above. There's also a Canadian production called "Blood Ties" that was shown on one of the cable channels here, and might be back for the new season. For some reason, I'm thinking there's a fourth show with the same type of theme, but maybe I'm wrong. I'm not as up on all the new shows as you are. Anyway, the one I was most interested in is New Amsterdam. But Fox isn't showing much faith in it, moving it back to mid-season at the last minute. So I wonder how good it actually is.