How can they make you default on your mortgage? Your payment is made of 3 things, the home loan, property tax, and home insurance. The Fed influences mortgage interest rates by adjusting the Federal Funds Rate. Even if it does impact mortgage rates, it would only affect the extremely small subset of people with variable rate loans.This still only impacts the home loan, not insurance/tax.
One of the hallmarks of countries suffering hyperinflation/other monetary disasters is lack of a central bank because the legislatures fail to wield the power responsibly. It is another check and balance, and virtually ever economically stable country has one.