You don't need to though: directed radio can be switched to point at different targets. In fact this would be preferable: i.e. blinking prime numbers out into the universe could be by switching radio targets to create the message.
Again, you assume that point-source RF which beacons to many places by switching aligns with when they're looking. You have to do a LOT Of hand waving around "better wiser Aliens can listen everywhere all the time" for this to pay off, and I would observe if this is such a brilliant technique, how come we haven't received the beams sent to us?
