The situation with AIPAC is not unique. Other American ethnic groups often lobby on behalf of a home country. Armenian-Americans tried to use their lobby (which also isn’t registered with FARA) to pressure Nancy Pelosi to have the US Congress recognize the Armenian genocide, at the risk of a rupture of US relations with Turkey. (I’m not taking sides on this issue, just recounting what happened). But then I think domestic US lobbies on behalf both of Turkey and of Armenia should register under FARA.
President Obama should ask Atty. General Loretta Lynch to begin proceedings to make AIPAC register, as well.