I think I understand what you mean, but I still think this is not a burn, at least not in the sense that I understand it.
I understand burning as a reduction of supply.
When the entire loan is paid, the debt that you created with the bank is settled, and the bank remains with the interest.
Yes, the bank gets the interest and remains with it.
But all the money you added in the principal are already in the pocket of the house owner. What was exchanged was some sort of a promise between you, the bank and the house owner. But no money was burned in this process. There was some promise made, that you kept for 20-30 years, to pay, and the bank got paid some interest because it supervised this payment process.
When a mortgage is created the principal is created from thin air. The buyer transfers that money to the seller of the house. He has to pay the mortgage back, usually in monthly installments. It is now his obligation to get money from elsewhere to be paid to the bank after which the principal portion is removed from circulation. The bank keeps the interest portion of the installment and only that, the rest is destroyed. Money is fungible. It makes zero difference that the money used to pay back the mortgage does not come from the seller of the house but somewhere else.
No money was actually burned. Which, like I said, is a problem.
Yes, money was burned = removed from circulation. What the bank keeping the interest causes, however, is that for no one to become insolvent, the money supply will have to grow continuously for all of the interest to be able to be paid. Yet, the total supply of money issued by commercial banks using this mechanism can decrease. If that happens, there will be defaults, which will be covered by the reserves held by the banks. But that even that is a separate issue from money being burned or not burned when a mortgage is paid back.
With that I agree. And when that principal is "removed" from circulation, nothing actually gets removed from circulation, because it was created from thin air, it was a promise.
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That's a philosophical notion, not a technical one. Technically, when a mortgage is paid back, parts of the principal get removed from circulation on installment at a time. The money supply shrinks a tiny bit as a result each time.