A minor nitpick: Do you think it’s number of vaults that matters or total storage space? It seems to me there are two dimensions that may be tweaked to manage this optimum, either as you say adding more vaults (and thus more space) or adding more space to existing vaults but no new vaults. A subtle point but one that I think is quite important economically and strategically.
I think the aim for the purpose of storecost is to have stable or increasing space but the aim for game theory / governance / security is (as you say) to achieve that by having stable or increasing vaults. Do you think this distinction is valid or maybe too close to equivalent to bother?
Worth noting this doesn’t invalidate your point, and what you say makes good intuitive sense.
Yes truly the important thing is total accessible storage space just as in btc mining it is total hashing power not number of miners. However if that number is not easily obtainable or can be lied about then total number vaults could possibly be a proxy especially if there is a min vault size requirement.
Those two objectives alone are not sufficient. Consider a pareto criteria to determine which system state is more or less optimal for the bi-objective maximization you propose. The issue arises when two conditions are equally optimal. Consider two extremes 1) A single giant vault capable of storing all the universe’s data or 2) an infinite number of vaults containing an infinitesimal amount of data in aggregate. These are both pareto optimal given only those two objectives. Additional constraints and objectives are required to have a satisfactory system. IMO the first two missing objectives to also consider are connection bandwidth and latency. (Hint: To think in 4D use XYZ and Color)
I remember there being discussion about having vaults be a standard size, with people wanting to give more space running multiple vaults. Is that idea dead?