I think the current system makes sense.
History shows that time and time again kings were desperately short of money. In the middle ages they had to borrow left and right and grant privileges to the cities to pay for their wars and building projects. In early modern times the kingdom of Spain went bankrupt... I don't know how many times, but a lot. In antiquity it happened that city-states or the Roman republic had to borrow money from the temples. In medieval times they borrowed from the church and monasteries.
It makes perfect sense to me that if you run a country and want a barracks constructed that it will take some months to raise the money, especially if your kingdom is a poor one. And if you're running a deficit because you have a large army and it's the start of the game... well, then you're obviously too preoccupied with trying to feed that huge army to be able to afford any grand new building projects.
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