...or, since the federal reserve creates money, they could do quite literally 100 strokes on a keyboard at the FED and repay the debt. A state doesn't fund itself through taxes, taxes serve many purposes but funding a state isn't one of them.

Ignoring, for a moment, the inherent and fundamental differences between an individual and a state...

...in my late 20s and early 30s I bought a new car.

At the time, that car cost more than I had in my accounts plus my other possessions at the time. In fairness, my annual income was more than the total cost of the car, buuuut I also was carrying tens of thousands of dollars of student loan debt as well, meaning my overall total debt was significantly higher than my annual income, or my "personal GDP" if you will.

Yet when I applied for my car loan, it came through with easy approval and I even qualified for the best possible interest rate.

Why? Because I've always paid on my debts adequately and promptly.

Nobody bats an eye when a couple buys a house that costs more than what they can cover with their combined income in one year. Why? Because that's an arbitrary and unrealistic yard stick of comparison and nobody expects them to pay off a house in a year. They're able to buy their house and live in it immediately, and pay for it incrementally, over time, as they earn over the coming years because of debt. And the bank is willing to lend the money because they'll make money in the long run through interest.

Similarly, it's unreasonable to imply that the US shouldn't carry more debt than it's GDP because the two metrics aren't directly linked in any way. And since the US has excellent credit worthiness, that debt is far safer than the bank's loan to the homebuyers. And the US gains access to borrowed funds by setting it's own interest rates through the Fed, which tells lenders exactly how much they'll make in interest if they let the US government borrow some of their money.

And since the US is a safer bet than homebuyers, that's why home interest rates are higher than the rate at the Fed: if they were equal, banks would never lend to homebuyers since they could get the same return by lending to the government. So instead, they set their own, higher rates for homebuyers, to account for the higher risk of lending to a party who has a much higher likelihood of default.

They said service the debt, not pay off the whole thing. For an analogy, your whole mortgage being less than your annual salary isn't a requirement; your monthly mortgage payment being a fraction of your monthly salary is.

The government is 100k in debt on my behalf