To answer the one sentence summary question, I would first correct and clarify not the simplifications made in the detailed summary, but the inaccuracies in the detailed summary.
First, be careful to distinguish between "Fractional Reserve Banking" and "Central Banking, the Money Creation, and the Balance Sheet."
Fractional Reserve Banking was defined in your link. Fractional Reserve Banking can exist with or without a central bank, or even without a government.
It means, when a bank takes a deposit from you, they might also write out a loan using those same deposits. For example consider the chain of events:
- You deposit 10 Gold into Bank of Stacks
- You go home, and meanwhile Bank of Stacks (BoS) has money in the vault. BoS wrote down that it "owes you" 10 Gold at anytime "on demand." One can conveniently think of this as a 0.0 day loan to the bank, at 0.0% interest, if one likes and it helps him think more clearly.
- Mr. Houseman goes to ask Bank of Stacks to lend him money to fix up his home.
- Bank of Stacks lends him 9 Gold.
- Bank of Stacks expects Mr. Houseman to pay them back their loan at least as fast as you might "call in" or "demand" your "loan" or "deposit," (using whichever term you suits your understanding.) Otherwise, you might get mad.
- Meanwhile, Mr. Houseman uses the 9 Gold he borrowed to pay Mr. Painter to do some painting.
- This is a critical point: Mr. Painter then deposits his 9 Gold into the Overflow Bank.
- Now, in the banking system comprised of Bank of Stacks and Overflow bank, the amount of Gold in the world is unchanged, but the amount of what we call "deposits" has increased by 9. Since in regularly functioning markets deposits are considered to be as good as money, or perhaps more precariously, one in the same, the amount of money is thought to have increased.
- If you could now rinse and repeat substituting Mr. Painter for You in the story with 9 Gold this time...you can see a money expansion that is independent of a central bank or a government.
A few foot notes on Fractional Reserve Banking: As you could glean from the example, there is really no limit to how much money could be created in a hypothetical world or perfect anarchy. However, today we have laws that state there shall be a limit to how much money a conventional bank can lend. They must keep 10% of all customer checking deposits "on reserve", implicitly for cases like where everyone might all on one day take all of their deposits before the banks can be repaid by their borrowers. This limit creates a limit to how much "money" or "deposit" can be "created" via the fractional mechanism. In the case of 10%, 10 gold could be stretched 10 times to 100 gold deposit.
These details are important because you must understand that a world without a Federal Reserve, indeed even a world when the legislature issues currency, would still have the question of how to handle "reserves." The Austrian economists tend to often theorize that in an absolute free market, banks would incentivize themselves to keep adequate reserves to meet demand; i.e. they believe banks would be afraid enough of a banking panic that they would use all their powers to prevent it, and keep a "safe" level of reserves. Others believe panic is inevitable, and that they should be able to dictate a high enough lawful reserve rate to prevent this. The may also believe this to be a good thing for inflation policy; a high reserve rate limits the amount by which a unit of 'real' money can 'expand' into increased deposits.
Reserve rates/levels aren't the prime concern of the Federal Reserve Bank of the United States, but consider what happens when they make one of their loans. All else equal, the deposits at the borrowing bank have increased. However, there is still no change, theoretically, in the amount of 'real' money. We don't use gold any more. Ask yourself now if there is any difference at all between money and deposit. It is unclear what a dollar really means any more, as former Congressman Dr. Ron Paul so often states; and if we don't know what a dollar is, then how can we distinguish between dollar and deposit? More to the point above, if deposits are considered money, then every time the Federal Reserve makes a loan, they are creating 'real' money which sooner or later may expand fully by ten times. (...Once again, all else being equal.) If the banks repay their "loan" to the Federal Reserve using expanded deposits that circulate on and on forever...Anyway, this should display the interesting entanglement between the Fractional Reserve Mechanism and the Central Bank, in this case called our Federal Reserve Bank. Again you must distinguish between the Fractional Reserve Mechanism, and the Federal Reserve System.
You said this:
When government intends to spend an amount of money they typically must acquire it by issuing bonds to a foreign country or by issuing bonds to the Federal Reserve for the cash that it prints. This inevitably ties money creation by the central bank to government debt.
This is not a good way to think. If a government needs money beyond what it collects in taxes and user fees for things like tolls on the road, then it auctions off bonds. It makes great overture, and so too does the Federal Reserve, to state that it does not issue bonds directly to the Federal Reserve. If people thought this were the case, then a great deal more of people would wonder what the difference really is between the Federal Reserve and the United States mint. Indeed, it would be little different than having the Congress print its own money. If the Congress issued bonds to the Federal Reserve directly, consider what would happen if it refused: it would be politicized instantly. Consider the opposite, same result.
Now the auction usually means anyone can participate. There are questions about what distinction of politicization there may be if a bank like old Bank of United States came along and bought a bond, and then simply turned around and sold it back to the Federal Reserve at a discount. I'm not saying this happened, I am just revealing different channels about which the meaning of the word "political" can be chastised or weakened.
This brings me to the question of legislative money or central planning money, and I would like to offer the idea of commodity money.
In today's climate, there is so much heat on every part of government. It may soon be that the Federal Reserve cannot dodge the politicization. In that case, is there any sense in keeping it around? If this were to be politicized, we might as well elect the people making the political choices? Laissez Economists like Peter Schiff often point out instances during the crises where it really did seem like Ben Bernanke, our current and then Federal Reserve Board Chairman, seemed to favor so and so over what's his name. (See Question: Why did Government Allow Lehman Bros to Collapse)
In the legislative mode, it is not at all clear about how our current politicians and our people would faire with money control. They could always just say "gold is money" and leave it at that. They could continue with paper, leaving an interesting scenario, especially over the long term. It is not at all clear how they would handle things. In a crises they could be inept due to the inherent sluggishness of democracy. But that assumes that "something must be done" at all by the government in a "crises." They may end up inflating too much, but then again, the people may smarten up in time to vote out the people that inflate too much. They may accidentally deflate. They may say "no money creation." This would be equivalent to a commodity standard, like the Gold Standard, when prices and interest rates fluctuate independently. This could theoretically be easy to enforce so long as the legislation was protective enough of its own longevity in order to promote predicability and stability. One may not want to waste time reading the tea leaves to see if there will be more or less money next year.
It is important to know exactly what money is, and it's no different than any other good and service that provides utility.