Good points, just bear in mind that the Arecibo message is not actually much of a serious attempt to communicate with aliens; it was more of a publicity stunt to celebrate Arecibo's reopening after having some new equipment installed. If it had been a serious attempt to send out signals that might be picked up by extraterrestrials, the transmission probably would have been aimed at more than one target, definitely at targets that were much closer, and probably at targets that were estimated to have a higher likelihood of harboring life. Plus it would have been repeated more than once! The Arecibo message was a single 167-second shout into the sky, pointed in a direction that was basically picked because it was convenient for the scheduled time of the facility's reopening ceremony. So it's not necessarily a good example if we're trying to consider this question. If a civilization (ours or alien) is seriously interested in sending out communications to other civilizations, the method we/they use won't bear much resemblance to the Arecibo message.