In the example you used, the tribal kingship would have a higher number of initiative points, but it's real ability for 'getting things done' would be comparatively lower.
Are you sure it won't be the opposite? The whole point of having a bureaucracy is to be capable of doing more things all at once. The main problem that could be observed in any advanced bureaucratic state is that lots of things get started, but few actually "get done"; in other words, the central government can only control its bureaucracy so much, and the bigger it is, the more factors emerge to complicate control and obscure observation.
My question is, taking this paradox common to all bureaucratic states into account, should a large bureaucratic monarchy have more initiative points or less? As far as answering that question goes, you seem to be saying that it should have less, but that they should count for more. Right?
In the Hundred Days Reform, the Guangxu Emperor attempts to spend more initiative points than he has, and as a result conservative forces take him out of power. If he had focused on simple military reform, or simple land reform, it would have been accomplished far more effectively than a more mobile, less organized Maratha state, for example, with less bureaucracy for implementation of reform.
a) You
can't spend more initiative points than you have, but you can stretch them as much as you'd like (within reason), though that will obviously dilute them accordingly; b) I'm not sure if the failure of the Hundred Days Reform had
anything to do with Initiative Points - it seems to have much more to do with various preexisting factors of internal politics; c) land reforms are never "simple", and I'm sure that a land reform alone would've been enough to piss lots of people off; d) even more irrelevant than c, but it's established tradition (Russian, Chinese, whatever), and probably with good reason, to do several reforms all at once, because usually, a society's problems are all interconnected and solving any one of them requires addressing the others at least partly.
Consider an initiative point as being useful for anything
That is how I understand it as well.
In general, a tribal kingship will have an army suited to that government philosophy: Fast and small. An absolute monarchy will have an army that is (comparatively) large and slow.
No, not quite. Tribal kingships tend to have a small and mobile elite (professional) force, or retinue, but it is always the nucleus of a much larger fyrd or what have you. Absolute monarchies tend to have a relatively small, but disciplined, professional, regular army (Louis XIV is atypical in this regard, due to both his ambitions and his resources; likewise the Hohenzollerns).
For another example, early revolutionary Bolshevik Russia suffered heavy territory losses to White forces due to its' low-power nature. As it stabilized and increased its' power, decreasing its initiative, the military effort improved.
As I understand it, Bolsheviks never had much of a lead in initiative as compared to the Whites; and their one key advantage from the outset was in what you call power. If anything it was a bit diluted in the early stages of the war due to rapid expansion, then was painfully consolidated again. Whites never had much "power" (due to constant suicidal squabbling and whatnot), but generally had the advantage in initiative (though ofcourse that was many different White factions fighting at once).
This was because of the resources at hand, not their government systems.
Certainly so, but I'm sure you will agree that war and history do not depend on available resources and luck alone; which is why I felt the need to try and single out Initiative.
They should constrain most players and if they don't, then there is no reason to have them.
What about making them assign clear priorities? This seems the best way to achieve that, all things considered.