Do you have a link for that limitation?
http://www.un.org/en/sections/un-charter/chapter-xv/index.html
"The election of the Secretary General is contingent upon the approval of the UN Security Council and is, therefore, subject to a veto by any of the permanent members. Neither Russia nor China would ever allow an American to become Secretary General just like the Western bloc of permanent members wouldn't approve a candidate from China or Russia."
There has been talk of moving the UN out of the United States to the Middle East...