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.
The ex-im bank is in no way required for political action regarding this concern.
If the ex-im bank is going to take a loss because a country is cancelling orders from US companies in mass, then the US government would likely contact the country via diplomatic channels to try to get these order cancellations to stop.
I'm baffled as to why you think the government needs the ex-im bank for an excuse to do this.
If this is the reason we need it, it is the flimsiest justification for it yet.
Creating a intermediary bureaucracy so that it can lose money in order to give a reason for foreign policy action?
Even the more obvious justification is better, as a means to extract donations from corporations to political campaigns, and a way to channel the extracted wealth of citizens to advance those interests. At least there is some perverse logic to that.