you are correct about the small and very small exporter........ I was both in days gone by
That is not relevant however because the companies larger than the very small do get loans and export sales that would have gone to foreign competition with loans guaranteed by their government ex/im banks
I recently performed a service to a not very large American company with for them large supply contracts on a foreign project. My several days work related directly to the specific transaction would not have happened absent the loan guarantee.
The benefits trickle down
That is true, to an extent. This is really a subsidy. So the question becomes: do you want to play the subsidy game with foreign state-controlled economies? By doing so, we become more like them. Large corporations take your argument, valid to a degree, and drive a truck through it.