One consequence of this is that our own solar system has been around for about 5 billion years, and is therefore probably unstable on timescales of 5-50 billion years. Indeed, long-term simulations indicate that there is a few percent chance that Mercury will get kicked out of the solar system
or crash into Venus or the Sun before the Sun dies in ~5 billion years  .
All in all, the Sun is just huge and wouldn’t be disturbed by any of it. Its gravity would tear things apart before an impact, just like the moon would be shredded if it came too close to Earth. Any sattelite has what’s called a Roche Limit, and if passes that it breaks apart from tidal stresses. That’s how you get rings around planets, and I guess a star too. Although in most cases you wouldn’t have a ring around a star, just burning fragments falling Sunward.
Never thought about it before until I read your comment, so I thought someone more knowledgeable than me could provide some insight here.
It’s like 400,000 times smaller than the sun. Worth maybe 5 billion coronal mass ejections, which are weekly events on the surface of the sun.
Figure the overall mass of venus is 100,000,000 years of CME ejecta all at once. But the sun’s gravity will override the planet’s hydrostatic forces and suck much of the planet beneath it’s own surface, in hours maybe. It wouldn’t dent the gravity well of the sun.
The atmosphere of venus would be gone before it reaches the sun. That might be the fun part. After that, the outer surface of rock on venus would melt and start to spew something like a comet’s tail, and then parts would peel away and drop into the sun like a large dark sun spot for maybe a day or so, as it gets closer. Eventually, a portion of liquified the mass would uneventfully fall into the center, and join in the sun’s general fusion reaction.
So it bothers me a bit that there is no actual fit and error margins.
It's #6 on the excellent (and surprisingly software-applicable) "Akin's Laws of Spacecraft Design": http://spacecraft.ssl.umd.edu/akins_laws.html
16. The previous people who did a similar analysis did not have a direct pipeline to the wisdom of the ages. There is therefore no reason to believe their analysis over yours. There is especially no reason to present their analysis as yours.
21. (Larrabee's Law) Half of everything you hear in a classroom is crap. Education is figuring out which half is which.
29. (von Tiesenhausen's Law of Program Management) To get an accurate estimate of final program requirements, multiply the initial time estimates by pi, and slide the decimal point on the cost estimates one place to the right.
30. (von Tiesenhausen's Law of Engineering Design) If you want to have a maximum effect on the design of a new engineering system, learn to draw. Engineers always wind up designing the vehicle to look like the initial artist's concept.
So I am not sure there is anything going on here.
(I know this is a lin-log plot)
There was an hypothesis about it being the remnants of a destroyed planet, but that was mostly an idea to support the Titius-Bode law, which was disproved a few hundred years ago.
 Currently about 3x Ceres mass, though it may have about Earth mass early in its history. See https://en.wikipedia.org/wiki/Asteroid_belt#Formation and https://en.wikipedia.org/wiki/Asteroid_belt#Evolution
Er... the Wikipedia page you're citing at  has this to say:
"Results from simulations of planetary formation support the idea that a randomly chosen stable planetary system will likely satisfy a Titius–Bode law."
"96% of these exoplanet systems adhere to a generalized Titius–Bode relation to a similar or greater extent than the Solar System does."
Once you've filtered out systems with two or fewer planets, you need orbital measurements with decent precision to tell whether a plot of planet spacing is actually linear on a log scale or not. Measuring a planet's orbit requires a decent amount of observation (since we can't measure star/planet mass directly and don't usually measure period directly), so unconfirmed systems likely don't have good measurements.
It's likely that most of the unmentioned systems get filtered out by one of the above two criteria.
Earth would we Sol#0
Kepler-90#-1.3, Kepler-90#-1.1, out to Kepler-90#0 for the outermost one on his graph.
That way, finding a new planet doesn't require either renumbering to specify where the planet is relative to the star. (BTW, I'm not real happy about using AU as the base measurement. It might be better to use Megameters since you're less likely to end up with negative log)
If the proto solar system's matter distribution was a Gaussian-like distribution, it would make sense that matter density droped in a logarithmic scale, and thus planets formed droped logarithmically w.r.t radius.
More intuitively.. further away from the sun has less probability for rocks/particles to interact with each other.
Jupiter, with 72% of all planetary mass, is more than twice as heavy as all other planets, combined.
Saturn, Uranus and Neptune take most of the remaining 28% (https://en.wikipedia.org/wiki/List_of_Solar_System_objects_b...)
(Of course, there also is way more volume that far away)
I recall one of the earliest breakthroughs in orbital mechanics was someone figuring out how the area of a slice of a elliptical orbit was the same anywhere in the orbit, when the angle of the arc is calculated as a unit of time and not degrees.
Not to say you’re wrong. I think you’re right, but the quality you’re attributing to the system is a behavior of the system that has an underlying link to physics that may already be well explored. Just nobody has bothered to put a pretty plot in front of us armchair types and students before.
That would be Kepler's second law. It states that a line between the sun and the planet sweeps equal areas in equal periods of time.
And calculus has an explanation for why that’s the case.
Regardless of your approach the sun is too big to usefully represent on the same scale and have all other objects be visible
It isn't on a log scale but this example is easy to see as a counterexample to the OP as there are two planets out in large orbits that orbit close together with a large gap between the first planet.
Obviously you hear things with your ears. And equally obviously, you can expect things in a simulation.