The proposed probes will be power starved, but they can use a very narrow beam signal.

A tiny craft can't make a focused radio signal. I suppose a laser com system would be possible, but even that would have a negligible energy density after 4 light years. My data point is that only the biggest dishes can communicate with voyagers now. Voyagers have orders of magnitude more power available, and are still orders of magnitude closer, than these probes will be.