New Horizons, to use your example, weighed a thousand pounds and used a 2 meter dish transmitting at something like 12 watts to compensate for the fact that the receivers are billions of miles from earth and hidden beneath a blanket of RF noise. The inverse square law can't really be beaten at that kind of distance so everything becomes inefficient by design.
If we can pick up that tiny 12 watt whisper of a signal from billions of miles away, surely we we could design much lower power omnidirectional signals that relay between mesh nodes closer together using far less power?
Imagine a string of probes that are all within a few thousand miles of each other with clear line of sight. Yes, we might need six million of them to cover that same distance, but if they were cell phone sized devices produced using what we've learned about consumer electronics it should be feasible to just keep launching them forever, for a few hundred bucks apiece, until we eventually build a large network that could assemble high resolution data by combining multiple sources.
We keep trying to fight the rocket equation, but that's not a battle that can be won. Mass is always going to be the limiting factor for space exploration, so maybe we can just start launching lots of intelligent low mass things regularly instead of the occasional big dumb thousand pound lump of metal.