There's no logical connection between centralism and decreased efficiency and it's not logical to say that a centralised government is less efficient because of distance or chain of command. Firstly, because distance is a non-factor these days.
Distance
is a factor. Being able to call someone and get an update, or fly over to somewhere once in a while is not the same thing as working in a situation on a daily basis. And really, how often do politicians from one state go look at other states? Rarely, and if they do it is merely for a speaking engagement.
Secondly because it doesn't necessarily require a chain of command if a federal department directly distributes its services without intermediary.
This sounds good, but is absurd in practice. Due to the size of the country and the amount of people we are talking about, there will be multiple people involved between the decisions and the application. The most efficient method is for the money to travel as little distance from the source as possible.
Even if you removed states as a governing body, then you would merely have federal regulators/management on the regional and local levels , and the money still has to travel all the way to the top before coming back down. In-efficient.
Thirdly and most importantly, to use your business analogy, management is often centralised despite distance because it's quicker, cheaper and more efficient to do something once at head office than individually in each store. Ie if each store is selling the same things, it's going to be cheaper and quicker to create an advertisement once for the entire chain, rather than allowing each store to separately create advertising. Likewise in government, why (theoretically) do you need 50 separate criminal codes when you could have one national code?
For the advertisement comparison, this is the reason the US Central/Federal Government was given the power over a common currency and common defence etc.
Why do you need 50 seperate criminal codes? For freedom of choice. One state could outlaw beer/drugs/tobacco etc, another state could allow everything etc etc. So whether you want to shoot/drink/smoke it up, or whether you are against the vices, you have a place to go. Different physical locales have different needs.
For public service, different states have different needs just like different stores in a retail company have different needs.
When I worked retail, we had stuff that sold and stuff that didn't. So obviously each month the store manager would order more of what sold and not order what we still had sitting on the shelf untouched. In other stores, those items that were left unsold at our location may have selling like crazy.
In a central management situation, one guy would look at the overall numbers and be like "send 15 x_item to every store each month, and 3 of y_item" when we need 20 y_item and no x_item.
Einherjar neatly simplified one over-arching ideal for localized government is that it keeps government close to it's purpose and source, which is the people.