Or at least minimized the number of business holdings that they have. Unfortunatley there would be no real fair way for them to do this, except to keep them from holding any other job or do any other business while they are president. It is the only real way to avoid conflicts of interest.
Even the slightest hint of corruption can cause a sitting president to be considered untrustworthy, as there is the possibility that foreign businesses can influence policies. The easiest way to make sure that isn't the case is to make it law that presidents and other politicians can't have foreign holdings.
Yes, an elected U.S. president should appear to be independent and should not be influenced by an international business. I believe the U.S. president is an important role model and the public expects him to be free from any form of influence from any international business. His office precludes him from getting and giving any form of special treatment to a particular business or company.
The President of the United States is a citizen of the United states of America. Citizens of the United States are afforded certain Liberties. One of these liberties is the freedom to conduct business abroad. Therefor as a United States Citizen it only makes since the president be allowed to conduct business in foreign countries.