The Syrian Jews in Brooklyn, New York are near-impossible to convert into. I don't see it as inconceivable some other sect banned it altogether.
Also, the edict is only since 1937, they were accepting converts earlier than that. So fundamentally they aren't a success story - they haven't been doing this very long.
Other Jews can marry in, but even this is limited. The majority of self-identifying Jews in the US would not have the qualifications to marry in. Any how, they are an insular community.