I wonder if it is all about money?
Not a comment on America, just entertainment in general - and your system certainly works in a different way than ours.
Surely BBC America shows the originals (BBC originals of course) but it just doesn't generate enough interest country-wide.
So the option is bought up (benefiting the BBC) and the channel that buys it has effectively a home-grown hit which has already been tried and tested and achieved a certain amount of appreciation nationwide. They reap the advertising revenue.
I don't know how selling a British made series would work in terms of revenue. I'm sure it must (countries throughout the world buy our programmes without needing to remake them) but perhaps it's less feasible in America. Certainly when the remakes are made, FAR more money is thrown at them then in our meagre budgets.
Just a suggestion - I admit I don't really know how this works
And after all you employ a goodly number of our actors in American roles, so I'm not claiming some sort of bias here.