A better strategy would be to recruit someone who already has access to the information you want. Consider the difficulty in "placing a loyal agent":
1. Getting them into the country setting up a life for them,
2. Getting them through citizenship (might take five-twenty years, might never happen),
3. Getting them hired at the CIA and hoping they get sufficient clearance,
4. Getting them moved in to a role with access to the information you want.
2,3,4 all require a number of things going right, nothing going wrong and each would take many years. Success would require a large number of attempts and the successful attempts might take over a decade before you get useful intelligence. I'm not sure anything like what you suggest has ever happened, the closest I can think of is the technique of placing agents in a foreign country and having them associate with targets of interest or report back intelligence[0].
Who are you most likely to have leverage over: An ex-national with family still living within your reach, that you can use as leverage? Or some anonymous U.S. citizen who's been pre-selected for their loyalty by the CIA, who you'd have to first identify, then track down their family or other leverage, then coordinate a hostage situation in such a way that they wouldn't just immediately blow the whistle?
I don't think either option is easy. The spy game isn't meant to be easy.
And similarly, I think you're greatly exaggerating the difficulties in obtaining US citizenship. It's a process that can take as few as 4 years. And thanks to our laws, people can simply have children in the US and they are automatic citizens.
And there's the third option that sort of meets both these opposite extremes in the middle and that's simply recruiting people already within the nation. Given the reported brain drain of the US intelligence forces, getting a substantial fraction of valuable targets (computer scientists, mathematicians, engineers, etc) into positions of intelligence does not seem like it would be all that improbable. Countries like China are already at a major advantage here given the huge numbers of Chinese involved in STEM.
Under which law? I thought this was debunked time and time again as an urban legend.
"All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside."
0: https://en.wikipedia.org/wiki/Fourteenth_Amendment_to_the_Un...