Do you have a human society to point to where your proposal exists successfully already?

Every single human society in history where a commons was maintained via a system other than centralized authoritarian violence?

In other words, every society that experienced periods not entirely ruled by an oppressive, authoritarian regime and that had/have some shared wealth whether it be in public spaces, public knowledge, public utilities, public education or other forms of public shared resource.

If we turn to the natural world it is very difficult to find ecosystems that function purely on a scarcity mechanism. If one considers the function of a predator in an ecosystem, it is precisely to stabilize an ecosystem so it can absorb large inputs of excess resources without the system collapsing. If one considers the basic function of herbivores in an ecosystem it is the same, to stabilize the growth of plants so that abrupt periods of resource abundance and opportunity don't destabilize the forest.

The only systems I can think of that function under the axiom that you suggest, which is that scarcity is a necessary obstacle to tackle before systems can resist destroying shared resources, are ecosystems dominated by invasive species and cancer. In both cases, it is the inability to tolerate abundance in a system because of an endless growth mechanism that causes the destruction of a dynamic encompassing stability. This is in a way how all dynamic stabilities collapse inevitably, but that doesn't mean that this is a fatal weakness, rather that all things that can be undone eventually do tend to become undone.

Which is all to say, there are systems that cannot handle abundance as a temporary state rather than a final destination never to be reached, but they are systems of cancer. All the dynamically stable systems we can point to whether they in the natural world or in human societies all feature some degree of scarcity, some degree of abundance and yet still manage to develop a shared commons of wealth.

For example, if you watch how Grizzly Bears eat Salmon, they do a shit job of it. They often become distracted in the process of eating a Salmon and just drop it leaving an only half eaten Salmon carcass on the ground wherever they happened to be. The way you understand how scarcity MUST impact systems cannot explain this blatant inefficiency in a natural ecosystem, individuals in nature are supposed to use EVERYTHING they can right? Evolution selects for efficiency right?.... Except it didn't because it turns out the Grizzly Bears discarding the Salmon ends up transferring a massive amount of nutrients from the Ocean to the Forest. The system benefits from slack, from a giving up of an individual boon for no perceivable immediate collective gain....

You cannot understand the essential aspects of the above example of Grizzly Bears, Salmon and Forests under the mindset that you are approaching this problem from. It would be a logical error of the system for a Grizzly Bear to waste effort beginning to eat a Salmon and then abandoning it for another animal, plant or creature to exploit. The Grizzly Bear should spend the minimal effort to catch only the Salmon it will eat in order to be competitive in an ecosystem that undergoes scarcity... but they don't... why?