Yes, all money is created in the form of debt, which implies that it has to be paid back with interest. There is no way for everyone to pay off all outstanding debt.
However, you are forgetting that not all debt is paid off. Some of it defaults, which destroys money.
But it's not the money which is being destroyed by defaults, it's only the debt component which is wiped clean. The credit component of the loan was already spent into the economy by the now-insolvent borrower and cannot be recovered by creditors so it's still circulating and adding to inflation.
It really sucks. What a horrible society we live in.
The current system monetizes bankruptcies. Bankruptcy is the only mechanism which allows debts to be wiped clean without simultaneously adding more debts.
This is untrue. There is also repayment, which is the way the system is designed to work. There is also voluntary/negotiated forgiveness by lenders.
More than that, how is bankruptcy a bad thing in this context? Isn't bankruptcy exactly what should happen when repayment becomes impossible?
Our system of bankruptcy organizes the process of default, and was actually the solution to the older problem of things like debtor's prisons.
This is incorrect. Repayment helps to clear the debt only from the perspective of the individual who has the debt but this is only possible because someone from the next generation took on even more debt to purchase the debtor's assets (took out a loan to buy the house, for example). So the aggregate debt never goes away, it's just transferred to the next generation and it keeps growing along with asset prices.
Asset holders see their capital increase continuously while non-asset holders keep getting squeezed until they are basically reduced to slavery.
Bankruptcy, however, clears the aggregate debt because the central banks end up taking the loss.
The only real purposes of taxation are to force people to keep using the fiat currency as a means of payment (maintain currency monopoly) and also to maintain scarcity of the currency as this helps to keep inflation under control (at least for consumables). But it doesn't actually prevent inflation in absolute terms because the government usually ends up spending more than it collects in taxes anyway (take loans from the Fed by creating new bonds); they mostly care about having inflation lower or proportional to other countries, not about preventing inflation.
The only way to pay off the debt would be to change the mechanism via which money enters the economy so that it is no longer tied to a debt as it does so. But then the question would be who should receive all that new debt-free money? Probably it will be big corrupt megacorporations via insanely large government contracts.