What was the real reasoning?
IINM there were two reasons given (actually one mainly for visiting, and another for moving there):
1. Not confident that would be allowed (halachically) to go out of EY once entering.
2. The ability to send emissaries and conduct activities in certain other countries.
It should also be noted that after the establishment of the State of Israel, the Frierdike Rebbe made an effort to be naturalized in the US (IINM the only color video of the Frierdiker Rebbe that exists, documents the ceremony).
ETA:
@Yehuda57 provided a more accurate and detailed response below.