BP are an abstraction for “how productive is our kingdom?”, and do not represent actual gold in the treasury. So the kingdom is growing and doing well with no tax. Congratulations rulers!
As for leadership role earnings, no rules exist, but a stipend of, say, 10 gp per month per leader per kingdom hex wouldn’t even dent a kingdom’s wealth.
Don't forget that whenever you withdraw BP for your own benefit your Unrest goes up.
Income Phase:
During the Income phase, you may add to or withdraw from the Treasury as well as collect taxes.Step 1—Make Withdrawals from the Treasury: The kingdom-building rules allow you to expend BP on things related to running the kingdom. If you want to spend some of the kingdom’s resources on something for your own personal benefit (such as a new magic item), you may withdraw BP from the Treasury and convert it into gp once per turn, but there is a penalty for doing so.
Each time you withdraw BP for your personal use, Unrest increases by the number of BP withdrawn. Each BP you withdraw this way converts to 2,000 gp of personal funds.
We had roughly the same thought regarding BP as what you're stating, but we also have absolute control over how BP is used and disposed, which means that either there are hidden taxes or, as is my favourite interpretation currently, the crown owns all means of production :D
Your leadership role earnings formula sounds reasonable, I'ma suggest it to my GM.
I like the “crown owns” interpretation, that’s a pretty good one. The standard interpretation, at least in my experience, is that it’s player decisions which determine what terrain improvements, hex claims, buildings, and armies get acquired/built, to keep the game of kingdom-building inside player control, but in the context of the game world, the rulers are guiding policy, but the citizens themselves ultimately do most of the work, out of their own pockets.
An example: the players decide to build a trade shop. In-world, the kingdom’s rulers have created incentives for tradesmen to move to one of the settlements, and some have, and have set up shop there. The players then decide to build a mansion. In-world, the rulers have suggested to some wealthy citizens that having a grand house to show off their wealth would be good, and someone chooses to do so, and hires a load of servants to work for them in the house and gardens.
That’s a known issue with the rules. There are a number of people who have expressed concern that “everything the players want works out perfectly” doesn’t reflect any sort of realistic outcome.
It’s possible to create a narrative where the things that happen in the kingdom from the kingdom building rules are the successes and you never hear about the failures.
Alternatively, Ultimate Factions from Legendary Games introduces some rules to allow simulation of other groups in the kingdom doing their own thing and trying to influence the kingdom.