There’s still the problem that two people can’t occupy the same space at the same time, so we need people to be able to swap places instantly. This then requires some coordination, which is mentioned below.
Some commenters have mentioned economy of scale—It can be more efficient to pool together resources to make a bunch of one thing at a time. For example, people want paperclips but they could get them much faster if they operate a massive paperclip-making machine rather than everyone making their own individually. I think this is already covered though, as if everyone has the same innate traits and preferences then they can all just operate the machine for one microsecond and collect their paperclip. This solves the coordination problem, as if everyone knows what they want and how much labor is required per person then they all just switch between each task accordingly. The only coordination is about who goes where and when.
So in the end, we have people indistinguishable by location, preferences, abilities, knowledge, and behaviour under any given local conditions. It seems that there is some sense in which the people in this world are ‘indistinguishable’ as agents (barring potentially unnecessary differences like eye colour). I think this hints at trade being unnecessary if and only if the agents are ‘indistinguishable’ in some sense.
Edit: We may also need need equivalent local conditions as well. If everyone wants a house within 3 miles of anyone else, and there is a single 3-mile-diameter circle that is the best spot in the whole world, then only one person could occupy that spot. If one person happens to have that spot, they could rent it out for a time in exchange for things they want. Boom, trade.
Or for a more obvious example, one person has all the military power. This person does no work and gets stuff in exchange for not killing anyone. It’s extreme, but probably technically an edge-case form of trade.
Some properties that I notice about semistable equilibria:
It is non-differentiable, so any semsistable equilibrium that occurs in reality is only approximate.
If the zone of attraction and repulsion are the same state, random noise will inevitably cause the state to hop over to the repulsive side. So what a ‘perfect’ semistable equilibrium will look like is a system where the state tends towards some point, hangs around for a while, and then suddenly flies off to the next equilibrium. This makes me think of the Gömböc.
A more approximate semsistable equilibrium that has an actual stable point in reality will be one that has a stable equilibrium at one point, and an unstable equilibrium soon after. I think an example of this is a neutron star. A neutron star is stable because gravity pulls the matter inward while the nuclear forces push outward. With more compression however, gravity overcomes these forces and a black hole forms, after which the entire star will collapse.