No the Government borrows against future taxes (consider that an accounts receivable), the borrowed money doesn’t have value because of consensus it has value because it is backed by future tax revenue.
If the government did as you say and borrowed a trillion per taxpayer the system would breakdown but not because of some “consensus” but because the account receivable (future taxes) is insufficient to payback the borrowed money.
Part of it, I imagine, is that the US government is likely to benefit from future tech booms, as it has in the past (despite tax shenanigans from the tech companies themselves). It gets a piece of stock market profits -- a stock market whose own levels are also currently out of keeping with rational revenue expectation.
To your point being rational doesn’t really give insights into these issues, but talk to any government budget officer and the can give you a sobering reality of the situation.
But it's not reasonable for that debt to grow without limit. It has to be able to pay the interest on the debt, for which it requires revenue. We take in only around $3T a year in total. That's still a large fraction of that $26T debt, but we're also supposed to pay our actual obligations out of that -- which at the moment are over $4T. Eventually the debt service is going to be larger than our revenue, and I just don't see investors being willing to just let that amount ride as new debt.
And yet people will loan us money for 10 years at well under 1% interest. That keeps the interest burden down -- and yet with the debt growing at over $1T per year it can't last forever.
This is one of two reasons it has value.
As other comments mention, the other reason is because it's by far the leading global reserve currency. Which is to say it's an attractive mix of liquid, stable, and available, compared to alternatives.
Furthermore, there are certain commodities (e.g. oil), for which dollars are required.
As a result, other countries / parties may believe the dollar is overvalued, but they will still have to acquire them, at the market rate, to execute transactions.
As a result of that ongoing demand, the dollar will tend to be valued both on its future tax revenue value AND as a result of a substantial, continuous demand.
Less than 10% of the total federal budget goes into debt payments.
The absolute numbers don't really matter, but the percentages do. Trends also matter, as long as they're considered carefully.
A pretty decent 10-year student loan right now is at 4% interest. And you generally have to pay it back with actual money that you earn.
A 10-year treasury note is at more like 1%, and nobody bats an eye at the government covering payments by issuing more notes. Meaning that, in effect, the US government is getting an indefinite interest-only loan at a pretty low rate.
Actual humans don't get to do that because of a sticky problem: eventually we age out of our money-earning years, and (hopefully some time later) we die. Lenders, understandably, have an interest in getting their money back before that happens. Or at least in getting to the point where the loan is collateralized by assets that are worth more than the loan's balance by the time that happens. And that's the ultimate reason why revolving debt gets worrisome: It's running down the clock.
The US government, on the other hand, is theoretically immortal. There's a risk that it might become insolvent at some point in the future, but there's not the same reason to worry about handling debt by endlessly revolving it, because there's no proverbial clock for it to run out.
Another class of entities that have a kind of 'forever debt' are large corporations. In general, they never want to be debt free. As I said elsewhere, it's about the percentages and trends.
To be clear: even this comparison has weaknesses. Indeed, US federal debt truly has no direct parallels.
Obviously, an individual human can't operate like this. The USA government can, and has for decades. Remember the Gospels' admonition to "render unto Caesar."
