The financial systems works different.
You seem to be conflating wealth and money. Money doesn't disappear from the system when someone fails to repay a loan. (Unless you are taking a rather wide, but still sane, definition of money, and hold that lending increases the money supply.)
No extra money needs to be printed to pay back all that interest. That's because central banks pay a dividend to their governments.
http://en.wikipedia.org/wiki/Money_supply#United_States
Also I am not sure what mechanism you are describing when you say that central banks pay dividends to their governments. On the contrary, governments like the US use their central banking system to do open market operations on bonds they issue to finance their operations, and usually have to pay interest on that debt. No?
Please see e.g. https://en.wikipedia.org/wiki/Central_bank#Currency_issuance:
"The European Central Bank remits its interest income to the central banks of the member countries of the European Union. The US Federal Reserve remits all its profits to the U.S. Treasury."
https://de.wikipedia.org/wiki/Deutsche_Bundesbank#Gewinn has some more information, but you have to speak German (or use Google Translate). Lower than expected profits of the Bundesbank have been in the news in 2011.
As with anything, too much of any extreme is bad. Too much inflation or too much deflation. But with fiat currency, it's natural to expect steady inflation over time -- especially if it's not tied to a commodity (e.g. after we got off the gold standard). That's because there's value in lending money to some enterprise, and that's the time value of money. Organizations with good credit (e.g. banks) issue and lend money to organizations with worse credit. So they will expect a return in the enterprise, and overall if they guess right, the enterprise will have returned principal + interest to the lender. If they don't then the money disappears from the system, but in most booming economic times, more money is created, and eventually more money is printed to provide more base money in order to pay back all that interest.
So it's like an elastic money supply that's being prodded by lenders / banks looking for a return.