You're right, your answers don't satisfy me, for example because your whole post is full of bullshit/misdirection. Not that it comes as a surprise.
> 1. Central banks are ranked on two measures: a.) How independent are they?
Central banks are never independent, because they're extremely central in governments' control of their money supplies.
> Are they easily swayed by politicians?
Of course they are. They exist to serve politicians (especially the shadowy figures behind the scenes), and massive financial corporations with first access to "free" (0% interest) money, with which to buy real, productive assets.
> b.) How well do they meet their mandates? The U.S. Fed is universally well-regarded in terms of its independence.
Universally, huh? We must live in different universes. Sure, it's supposedly a "private" entity, but obviously married to the government, buying treasuries like there's no tomorrow.
> It does less well on its "dual mandate."
The Fed's "dual mandate" is supposedly to control interest rates and employment. Too bad it can't create jobs - the best it can do is stop fucking with the economy and let businesses create jobs. Interest rates have been zero (or near it) for years, in an attempt to maintain and create bubbles to keep that inflation going, to lighten the government's debt load etc, and to maintain the illusion that the US economy is not in shambles. It is.
> 2. Central banking systems make cash and checking possible
Oh, right. Because gold wasn't used as "cash" for millennia before central banks entered the picture? Money is just a medium of exchange, and gold was used as one exactly because its properties make it suitable for it.
> Without central banking, your bank-denominated money (whether "checking" or cash) is valued only to the extent that a third party trusts your bank
No, without central banking, my medium of exchange works just fine. That's why it's a medium of exchange - because it can be exchanged for stuff.
> Your twenty dollar bill printed in Philadelphia becomes valueless in New York, 100 miles away. Fixing this problem makes business transactions, particularly lending, easier and more efficient.
I'm not sure how to decipher this.
> 3. Broadly, fiat currency is valuable because other people deem it to be so.
Almost. Fiat currency is valuable because other people are willing to accept it in exchange for goods and services.
> Specifically, even if no other person on earth wants it, the IRS and the courts will accept it.
In fact, they will downright demand it. Governments will forcefully confiscate a percentage of what you earn, and strangely enough, they all want to get it in a specific fiat currency. Go figure.
> Being able to pay my taxes and satisfy court judgments against me in fiat currency places a floor on its value
Being forced to pay taxes in it does that. This, incidentally, was my point earlier, as I suspect you knew all along.
> 4. Ability is not action. It is a problem when and if they do happen to do so.
Oh? Does "QE" ring a bell? .. What about QE2? Or perhaps you're familiar with the still on-going QE3 they're talking about "tapering" to something like "only" 75 billion dollars per month in freshly created thin-air money?
You're so full of shit it stinks all the way to Finland. Again, not a surprise.
> Secondly, we want the money supply to rise and fall with the economy.
Who's we? And no, "we" don't. In fact, in a free market, the rising and falling of the money supply would be negligible because whatever would be used as currency could not be manipulated by anyone (by, say, pressing a button and conjuring 666 trillion quatloos into your account).
No one actually wants to use fiat currency, because it's manipulated at will by governments.
> 5. Because the prior standard for currency, precious metal, was dangerously uncontrollable.
Being uncontrollable is one of the fundamental reasons why gold was used as currency, and it's a fundamental reason for why Bitcoin has become so popular. Here in the real world, we really want our currencies to be uncontrollable by anyone.
For someone who's studied "how money works" for years, you sure are clueless about it. Of course, you might just be a government shill, out to mislead people.