The word 'just' is doing a whole lot of work in that sentence!
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.
Each one needs whatever sensors, but more importantly, the auxiliary stuff to last years or decades in transit: in particular power supplies, heaters (=power!) if you can't make your electronics survive constant cryogenic temperatures, as well as comms amongst themselves to organise the mesh and high-gain comms back to Earth.
Maybe the worst of that could be solved with a nuclear power supply and then it's basically "just" radio and software design.
I also don't think you'd use onmidirectional mesh comms, you can get a lot of milage (literally) out of a phased array that can steer the beam at each target, plus it also becomes a bonus multistatic radar network.
I suppose that's my point. It's really just a series of maybe-not-that-easily solvable engineering problems, and it would allow us to not only explore further but to do it at a relatively low cost and with the ability to "upgrade" the network gradually as each generation of probe improves. More importantly, it would allow us to finally get around that pesky rocket equation and do it cheaply enough that we might actually get political buy-in.
> nuclear power supply
This was my exact thought, a small RTG power supply in each could provide enough power for hundreds of years with no moving parts. Not enough for billion mile transmitters anymore, but now they don't have to be.
> phased array that can steer the beam at each target
That's a great idea, and like most of the individual pieces of the plan it's kind of a thing we already know how to do. Sure, you could dedicate the next decade to solving it well, but you COULD solve it today with variations on off the shelf systems.
Really, the power source and antenna design are just a few of several hundred (thousands?) of engineering problems that would need to be solved, but all of the engineering challenges I can think of are solvable with variations on current tech.
The only reason it isn't being done is that nobody is doing it.
They don't launch space probes out of cannons because they don't make it out of the atmosphere. According to [1], muzzle velocity of a cannon is about 1685 ft/sec, which is 0.51 km/s. Delta-v to orbit is around 10 km/s. This is a feature, though, because launching your cannon shell into orbit means it isn't hitting it's target.
But let's suppose you have some propellant that is 20 times more potent. A cannon imparts all the energy at the beginning, with the acceleration happening as the expanding gasses push the projectile out of the tube. Assuming that the probe survives the initial explosion (unlikely), it is going to accelerate to 10 km/s very rapidly. Once calculation [2] put the g-force on a cannon shell to be 15 g, but lets say 10 g to be conservative. So we need 20 times more acceleration, so 200 g. Even if your probe is not smooshed in the acceleration, it is unlikely to be functional. (Note that, in comparison to cannons, rockets avoid this problem by providing the acceleration over a long period of time)
Now if you managed to engineer it for 200 g, air friction is going to burn it up. We know this because when spacecraft come down they have to lose all the velocity they got going up, and they tend to burn up. Heat shielding is almost certainly going to put you over the weight limit.
What, you say? This is a space cannon? Okay, well leaving aside how this cannon is going to burn the propellant without oxygen, the delta-v to Pluto from LEO is 8.2 km/s, so Sedna will be a little bit more. This is still an order of magnitude larger than the cannon, and still has acceleration problems. Plus, you had to use a rocket to get the payload to the cannon, so putting a second stage on the rocket.
You still have the issue that it's going to take a couple of decades to get there, which is what this paper is trying to address.
[1] https://www.arc.id.au/CannonBallistics.html
[2] https://math.stackexchange.com/questions/3249185/calculate-g...
More importantly, I would like to point out that while all of your concerns are valid, many of those problems were already solved in the 1960's. Project HARP[1] was able to use a 400 lb projectile to launch a 185 lb payload to a height of 111 miles... in 1966. We don't need anything close to 185 lbs of payload.
You'll note that 111 miles up is considered suborbital space. HARP was built mostly of 1950's era technology, and cost between $1000-$3000 per payload to fire. It had a 16" barrel and could be reloaded in about an hour. The payloads were encapsulated within a "sabot" to protect them, and the sabot seemed to do it's job, because primitive electronic instrument packages were deployed without being destroyed and weather balloons were deployed with success.
The long term plan for that project was to add a second stage which would push the payload into orbit, or beyond. There is no reason to believe it wouldn't have worked, but the Vietnam war happened and people lost the taste for funding space exploration. It was shut down. The enormous gun is still there, rusting where it was abandoned after firing nearly 100 ballistic payloads into suborbital space
Now, if we could fire ballistic payloads into suborbital space in 1966 what do you think we could achieve today? Honestly, the engineering isn't even that difficult, it's just a matter of figuring out how to pay for it. The rest is an incremental improvement over something we could already do in the 60's.
Sure, I'm glossing over a ton of minor issues (like the entire second stage), but those problems are also basically solved and we've learned a few things in the last 60 years. I not only think it's possible, I think someone should give it a shot (pun intended).