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).