I'm with you. The stems aren't the problem. Although the foilage is very nice, other plants that you plant to come up after the poppies are gone, have to do so through that jungle. Once the oriental poppies are finished with their bloom, you can safely cut them back to the ground. You will get some regrowth (typically just a basal rosette, not full sized leaves) later in the season that will remain tidy until fall.