Especially once you reach the “hundreds” level then given the technology exists and the people exist why would it stop, until there’s nowhere else to go.
There is the light cage issue where a civilisation can only spread so far with exponential growth before internal pressures overwhelm it (the leading edge never gets a chance to continue as it is overwhelmed by trailing edges)
Even in that situation though you’d still have self replicating probes - likely at a far lower tech level than biological. Once you reach the tech to send one probe which can duplicate itself more than once using resources in a new system then its game over.
Send 50 probes to each of the 50 stars within 15 light years at 0.01c. If 10% make it they then use local materials and send 50 more, that’s 250 out in 1500 years. Then it’s 1250 out in 3000 years. Within a few millennia years you’ve got millions of probes spreading in an unstoppable way. The ones heading back “inwards” will fail, but those heading outwards will reach each new star dozens of times, only one will need to get there. Within 10 million years you’ve reached the entire galaxy.
To stop it you’d have to make a self replicating probe which was faster and did exactly the same thing and caught the earlier probe, but then when would that probe itself stop, it would have no way of knowing if there were any other “bad” probes to find without becoming the bad probe itself.
Living beings are the same. Once a few dozen have made it and passed on, it’s inevitable it will continue. It may leave out a hollowed husk in the origin point with all resources having being consumed in the centre, but that doesn’t matter as the centre has no way of affecting what happens on the edge, and one edge has no way of affecting another edge.
I think you may be expecting an exponential growth when population dynamics almost always favor logistical growth. At some point your machines, or your colonial behavior hits a limit and your growth starts to slow down. I suspect that limit is within the solar system for the vast vast vast majority of civilization. And even if one escapes their own solar system and starts anew on a new home world, they most likely will not colonize another. The space is just so big, and habitable worlds so far away from each other that I find it extremely improbable that any civilization (and their ancestor civilization) will survive more than 5-6 colonization (by far most will see 0).
> Living beings are the same.
They are not. You are describing living beings like viruses (fair enough; viruses are worthy to be considered lifeforms) that spread from host to host until they infect everybody. But viruses don‘t behave like that. The vast majority of them only infect their closest neighbors, and those that do spread towards the limit of all members of the species (like Covid) still fall short and eventually start to slow down their spread in a logistical manner. Growth only looks exponential while you are at the initial stages of spread. This behavior is not only common among viruses, but in fact most population dynamics can be described with logistical growth.
Well pack it up folks, we've been told what would be possible for any alien civilization, even given millions of years of effort.
The only argument for von Neumann probes that I can think of is as a specific answer to the Fermi paradox. The universe should be filled with these probes, but since it obviously isn’t, we can infer that no civilization has reach the interstellar age.
I reject this framing, the Fermi paradox is only a paradox if you assume that space colonization is a thing that is not just possible, but inevitable. My solution to the Fermi paradox simply rejects this assumption. Civilization will not colonize definitely, they will do their space explorations with telescopes and targeted probes, and they won‘t build any von Neumann probes (at least not ones continue to replicate for dozens millennia).
Aside: I am aware of the irony that my description of civilizations outside of our solar system is also a fantasy.
I also think fast space travel (like 0.1c) is rare among civilizations, and may only happen in the order of hundreds of time in the history of some civilizations. And most of these fast space travel will scientific instruments for curiosity and exploration, not for colonization. And that a technologically advanced civilization would favor doing their explorations with telescopes, not probes. So probes would only be sent long distance for rare occasions.
This would mean that almost no civilizations will be expand beyond their solar system, and those that do, will only do it a handful of times, and the expansion will finally stop.