Yes, select all and then exporting objects (like primitives) is sort of the same thing as doing them individually for selecting filenames, except that you don’t have to manually find them all in the scene. The DAZ Studio bridge, for objects like primitives, does do everything at once though.
Unfortunately for trees it looks like you are out of luck. They don’t appear to transfer correctly across the bridge, and if I select multiple trees and try to export them, it appears to only export one of them, unlike primitives where it did multiple exports in a row.
Perhaps somebody else has another idea?