It seems to me that most levels of government should be "outward-looking"; the primary activities of my Federal Government should be centered on representing me to, and defending me from, other governments. Trade, defense, immigration are areas that seem suitable responsibilities for a Federal Government.
Likewise, my state government should be representing me in dealings with other states. Regional concerns like pollution, water rights, shared resources, might be within the states' purview.
Any government unit that intends to concern itself with an individual citizen's day-to-day activities should be small enough that the personnel who are responsible can know each citizen personally. This means units as small as County level in sparsely populated districts and even as low as ward-level in heavily populated urban areas. These should be the only "inward-looking" governmental units.
This is not to say that governmental units cannot cooperate in things like the transfer of information about crime and criminals. The important thing is that the information should be maintained at the level where action is taken. Modern networks would allow queries to be made of distributed local data.
Another area of useful cooperation is the setting of standards: weights and measures; uniform codes; model legislation. It's nice to know what a pound or a kilogram is; it's nice to have traffic lights be the same color from jurisdiction to jurisdiction; it's nice to be able to consult a standard when you want to produce something, so it can be sold anywhere on an even basis. Standards should be set FOR VOLUNTARY USE at as high a level as possible. If a standard cannot command acceptance merely by its very usefulness, what good is it? People and organizations that falsely claim to adhere to a standard will be found out and the market will decide their fate.
The advantages of this form of organization are responsiveness and efficiency. You can't send taxes up, and benefits down, a hierarchical ladder without paying people to collect, manage, allocate and administer the money. These people are NEEDED to operate a massive bureaucracy, yet they produce NOTHING. You can't eat, wear, or live in, the results of a bureaucrat's efforts. Yet he must eat, wear, and live in, the results of your efforts. And a bureaucrat who never heard of you cannot possibly be responsive to your needs on an individual level.
Money and authority should never go higher up the ladder than required to get it where it is going. If 100 people are going to support 5 or 10 people in need (for sake of argument), then why should their support go to pay the salaries of the half-dozen tax collecters and welfare administrators required to move that money up and back down the entire hierarchy? That dilutes their support by as much as half! One person could manage that money in a small community and that person would KNOW PERSONALLY those who were in need of support. This would cut most of the waste and fraud out of the support of those in need. The same is true of other wealth-transfer functions of government.