I have had trouble getting some storage emptied when there's trucks assigned. The trucks just sit there, and do not do anything - even if there is an assigned export target. It is frustrating.
It could be helpful they'd alert with feedback if there's something wrong - and explain what they what they would need to function. That would be helpful.
I am able to eventually get things emptied through priorities. But it's logical that if there's a truck assigned they would export things.