There are several problem with your theory. Most importantly those in power don't know how long they will stay in power. Dictators don't last that long on average and if you assume there is a 50/50 shot your going to last 10 years investing in the economy may not actually benefit you. Secondly taxes are just one of many ways that the connected extract resources from society, often favors or bribes are an easier target for those with some but not total power.
Finally, the state's real power has little to do with direct force. Functional society's run on softer forms of coercion. Such as propaganda, tribal allegiance, religion, or even entertainment. Consider, over 10 million people live and work in america without permission from the government to do so. And even those with citizenship the largest crop in many states is marijuana and such income rarely makes in on the old tax forms.
Finally, the state's real power has little to do with direct force. Functional society's run on softer forms of coercion. Such as propaganda, tribal allegiance, religion, or even entertainment. Consider, over 10 million people live and work in america without permission from the government to do so. And even those with citizenship the largest crop in many states is marijuana and such income rarely makes in on the old tax forms.