Let's use a simple example.
Fed loans US gov 1bil + 1% interest.
The US gov now has 1bil. Where does it get the 1% interest portion from to repay the debt? It has to be created first via someone else borrowing it into existence.
Assuming the U.S. tax base is productive enough, the 1% interest can be paid from production. It does not have to be paid though additional borrowing.
Now the US gov repays the fed, but what about the new borrower? Where do they get the funds from to repay their debt + interest.
I assume you are referring to the problem that if all U.S. debt is paid back, there would be no more dollars. That is only a problem if the new borrower's debt and interest must be paid with dollars, and that problem exists with any currency -- even a gold-backed dollars, since no dollars would exist that could be bought with gold.
Every new loan must be collateralized by something, hence if the economy does not expand fast enough to create new assets as collateral we get credit inflation. Existing assets must be artificially revalued higher in order to support new debt. Think of home prices, the underlying value of the home never changed. If you read the original Fed Reserve act, holding US government bonds was illegal. The fed could only lend against SHORT TERM self liquidating bills from the private sector. Ie The fisherman's IOU's would be the collateral for new fed credit. This was changed when they ammended the fed reserve act in the 1930's. Banks got in bed with the government and slowly Tier 1 capital assets became government bonds.
Gold's role was to extinguish debt. I bring a bank note(LIABILITY) and exchange it for Gold(Asset). Do you see the difference with your example? I am not extinguishing 1 form of debt(liability) with someone elses. Money is anything that extinguishes debt. It does not have to be gold, however ONLY production can repay debt. Everything else is merely a form of credit. We do not have "money" present in our system, it was removed in 1971.
A healthy bank backed its deposits by 2 things. Gold and real bills(self liquidating credit which matured into gold). This required trust, now trust requires prudence which is a virtue. You had to be sure the fisherman would make good. The economy could be expanded to the extent of your prudence. This is a functioning free market system. Money is backed by the productive capacity of your economy. We have nothing of the sort today, hence the boom(counterfeit credit) and bust nature of our system.
The reasoning behind gold was simple. Gold was and is the most saleabile ie liquid asset. You could get rid of large volumes of it without depressing the bid side. Real bills were the second most liquid credit instruments, since they matured in gold and were backed by real production.
I agree with you about the value of a gold-backed currency, but you lost me here. How does this relate to the belief that the principle plus interest exceeds the money supply and therefore can't be paid off?