The greater the distance (and time) to the recipient...
...of a message, the less useful the project becomes. Since this method targets such a very small percent of the sky (and the percent covered is random) it would be seen by very few neighbors, and more and more long-distant friends as the millenia mount.
For an engineering project as costly as this (sending), you would want a payback. Message in a bottle altruism is cool, but we would not pay much to support it. And I doubt that ETIs would, either.