The reason the government is involved in the export-import bank is because other countries could economically attack the US if they were to engage in a trade war. If a country (say China) were to get it's companies to order a lot of American products with no intention of paying for them nor taking delivery of them then the US government can use it's political influence to get this to stop and reverse this policy of China (in this scenario). The private sector would not be able to exert this influence.