> If a bank takes a $1,000,000 deposit one customer, and lends $850,000 of it to other customers, there isn't $1,850,000 worth of money all of a sudden.Not all of a sudden, as in instantly, no, but there will be. See below.
> There is $850,000 worth of debt held by customers, and another customer with a $1,000,000 balance
Yes, but what do those other customers do with that $850,000 of debt? They either deposit it in another bank, or they use it to pay someone for something, and that someone deposits it in another bank, or...
In short, virtually all of that $850,000 of "debt" ends up as $850,000 of additional bank deposits in other banks. And to those other banks, those deposits are simple deposits--there are no debts (yet) against them on the other banks' books. So there is nothing to stop the other banks from lending out as much of that $850,000 as they can again. Which means the other banks have just turned what was $850,000 of "debt" into $850,000 of new money.
> Fractional reserve banking doesn't create money out of thin air
Yes, it does. I just explained how.
> it's just a system that allows for deposits to be put to productive use
More precisely, it's a bad system for putting deposits to productive use, because it mismatches maturities and therefore leaves the entire financial system open to bank runs, which then have to be prevented by additional "protective" measures. Which will sooner or later fail, and fail all the more catastrophically because the protective measures enable financial institutions to hide the fact that bad investments are being made.
The correct way to put deposits to productive use is to make them time deposits, not demand deposits. In other words, if you have a spare $1,000,000 that you have no good use for, you deposit it in some financial institution for a period of time, say a year, or 5 years, or 10 years, and that financial institution promises you some particular rate of return over that time in exchange for the use of your money to finance productive endeavors. Of course this is just another way of describing a bond, or a certificate of deposit, or a money market certificate, or whatever your financial institution chooses to call it.
But suppose you buy, say, a 5 year bond with your $1,000,000, and then, a year later, you find you need the money? Well, that's what a bond market is for--so you can sell your bond, at a fair market rate, and get cash in exchange, while someone else has now invested their money for the remaining term of the bond. There is no need for the financial institution to treat your $1,000,000 deposit as a demand deposit, withdrawable at any time, while it is transforming maturities by investing that money in other productive endeavors that take time to mature, just to shield you from unavoidable uncertainty about the future. There is certainly no need to expose the entire financial system to possible collapse to do this. The only reason this wacky system persists is that people in power benefit from it, and ordinary people have gotten so used to it, since it has been around for so long, that they don't connect it with the occasional meltdowns that it causes.