Sounds like a good plan to me, and also it seems to me that all government offices, especially the exectives have been packed with Demoncrat liberals. The ability to fire federal workers is crutial to any change and both parties should have a better more equal representation in both the executive and lower level managment branches of all these agencies.
Some interesting history. Until 1906, the feds had very little to do with naturalization. Naturalization could be done by any court of record. In 1906, the Bureau of Immigration was expanded to the Bureau of Immigration and Naturalization. The law that did this prescribed standard naturalization forms, and encouraged state and local courts to surrender naturalization jurisdiction to the federal bench. In 1913 the bureau was split in two, just as we're discussing. They remained separate until 1933, with the creation of the INS. After that, the INS received more and more responsibility over things internal to the United States, many relating to wartime measures.
That's what's really changed the agency, IMO. The weigt of these internal responsibilities has rendered border control ineffective.