Again, you are assuming your conclusion, and you do not even do us the favour of stating premises, which is hardly conducive to a productive discussion (or, any, really). On the other hand, it is quite fundamental to welfare economics that under a few assumptions, some unrealistic and some less so (namely: perfect information, fully internalised externalities, absence of market power, local nonsatiation and convexity of preferences and production) it is possible to reach any point on the Pareto frontier. The policies required to reach a desired point in such a toy model is left as an exercise for the reader. Now, the actual juicy questions here are how things like market power, externalities and imperfect information affect this? Is the model still a good approximation? To what extent are we able to correct things, and do we even want to? If we do, how best to do it?
> The "natural mechanism" of "fair procedures" in the case of systems wherein parts attach to other parts based on their current size
Again, you assert that it's "natural" and "fair" as if the result is a foregone conclusion. If it is inevitable that dx be a f(x) ~ x then yes, that's an exponential. Why would it be unnatural or unfair for dx to be instead a function of y, some other factor that has no proportionality to x? You are stating as a conclusion and premise that financial wealth experiences preferential attachment unconditionally, that is in essence, circular reasoning. What is the actual mechanism, the force, and how irresistible is it really? Would resisting it simply divert its effects to something else, for example, concentration of political rather than economic power?
Quite frankly, the dismissal of everything outside of a frankly ridiculously narrow space, where your model with an unspecified mechanism (which does achieve the results that you say it does) clearly must be an accurate reflection of the real world in all circumstances... Well, it gets old quite fast. If you really must use that model, describe and justify the accuracy of your proposed mechanism at least, if you please.