Wasn't house of cards British.
To be air the BBC does a lot of good stuff, the just don't become terribly well known or well remembered because the series are short and sweet. Hustle, Spooks were fantastic but short seasons and they ended it on a high. The problem with Americans is they run stuff into the ground. Remember house? That was great, but then they churned it out season after season until eventually it was like "ahh I wonder what's wrong??? of course it's ****ing lupus again."
Like other people have said the BBC has relatively little funding by comparison, the cable networks have adverts every 4 seconds and a massively increased viewership. Not to mention the networks only do entertainment, not news and online interactive stuff like red button and i player stuff... not to mention all the amazing live stuff the BBC airs that the cable networks don't have to do.
Also you're saying why don't the BBC have big stuff like walking dead and game of thrones... don't forget they're all different companies funding their own star series, AMC, FOX, HBO, Warner etc so only effectively having to put their eggs in one big basket.
You're giving the BBC a pretty unfair wrap considering all the awesome stuff they do that the companies you're comparing them to wouldn't even have the structure or forethought to consider.