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The prefecture will pay for itself in 3 days (even with a margin), not 5. Therefore, the rest of your statement doesn't hold any "value."
Ley, how did you calculate? You divided 2500 by a thousand:D :D :D But you should have divided by 500, because building a prefecture gives your kingdom an incremental income increase of 500 gold...
In short: money today is worth more than money tomorrow.... That's why five days isn't entirely an objective measure of investing in a prefecture...... But never mind, here's what I'll say:
From an economic (i.e., even ignoring tactics) point of view, buying any hero with "+350 gold" is more attractive than building a prefecture.
Firstly: with the hero, you also acquire an army, which also costs money. So, when you calculate the payback period, you should correctly reduce the cost of the hero for calculations by the cost of the troops purchased with him. Then, if the hero has more than 750 gold worth of monsters (which seems to be the case with all "+350" heroes, if you look at the creature descriptions), then they are "more interesting" from the point of view of investment.
Secondly: the hero brings you resources, chests, external dwellings, participates in quest chains, and can ultimately develop "assets" - i.e., brings additional benefits that you shouldn't ignore either... (and here we can think about how much 1000 gold is worth on the first day of the game, and how much it is worth at the end of the first month)
A special case is when you have enough money for both the prefecture and the purchase of a "+350" hero.
In short, the statement that investing in the economy of cities in the early game is a beneficial undertaking is far from being an absolutely correct statement.