The analogy has always been strained, since national debt just doesn’t work like personal debt.

Also, when you can borrow at sub-inflation rates, there’s rarely an incentive to stop.

It's the Bank of Japan who decide the borrowing rates, so, not problem in that regard.

Ok, but they don't control inflation. At some point, I think it's obvious that printing money becomes counterproductive. But where exactly is that line?

The Bank of Japan, can actually control inflation, because, as we have determined, they control the interest rate. Also, if necessary, the government could raise taxes and run a surplus to diminish inflationary pressures.

But those are moot points, because the problem of Japan for the last 20 years has been deflation, not inflation. Despise that, as you can see in the comments here, there are people that still predict inflation in the future.

They don’t control inflation. But all of the warnings about hyperinflation being “right around the corner” have remained hilariously false. So who knows?

They only control their inefficiency around an increasing trajectory

It's not debt, it's only a number that reflect the accumulate of past government deficits.

A government is the issuer of the currency, so, nothing to do with the debt of a household or a business.

What if we alter that analogy to a person who makes 100k/yr with a 110k mortgage, and next year they make 101k with a 115k mortgage, and next year they make 102k with a 120k mortgage, and so on?

Then I think we should rename it from "mortgage" to "student loans". As long as they keep making minimum payments, this is technically fine.

Misses the point, but sure, "student loans" is a fair comparison. The name doesn't matter to me, it's all debt.

I don't see it as "technically" fine that the rate at which the debt grows consistently exceeds the rate at which the income grows. There comes a point in time in which the principal of the debt is large enough that minimum payments exceed income.

The US government doesn’t make 100% of GDP. GDP is $21 trillion. US government takes in $3.46 trillion.