The Americans is a cool show, but the real life illegals could not fool anyone.
These days Russia probably has no need for this type of presence, since there are enough Russians living in the US and enough of them support Putin that a small percentage may choose to work as spies. Same for China.
Another interesting detail that came out of the 2010 illegal bust was that America is so diverse and people are so respectful of privacy, that one of the spies was doing just fine with an American name ("Jack Ryan" or "Patric Foley" or something like), fully American "legend" and a heavy Russian accent. People wondered but nobody asked any questions.
P.S. And who needs spies when you can have a whole administration? :)