Should it stay or should it go? It is little more than thinly disguised corporate welfare.
It should go. Its just another market distorting corporate subsidy at taxpayer expense.
If it were to go wouldn't it put American companies (and the US economy) at a competitive disadvantage? Hint: the answer is yes because most other industrialized countries have similar subsidies. The result of shutting the ex-im bank would be that the US economy would grow less then it otherwise would and jobs would be relocated overseas that would otherwise be competitive in the US.
The selected companies yes (thats also why it will continue). But other companies, and the public will win, by not paying the cost of the subsidies, and by receiving valuable goods from abroad, and from non-distortion of the markets.