What's the point of comparing quantities expressed in different units?

Debt is in dollars, GDP is in dollars per year.

A ratio (e.g. 100%) of quantities expressed in different units can be useful. "How many years of GDP is the debt?"

Miles per gallon is another example. It's a useful number.

GDP provides a rough measure for how fast a country could drain its debt—similar to looking at debt-to-income ratio when issuing mortgages to individuals.

Interest is a percentage of debt.

Income through taxes is roughly a percentage of GDP.

You could also just compare interest spending vs budget, and lots of people do. Spending on interest is roughly $1T out of a total $7T with income of $5.23T

$1T of an incoming $5.23T is pretty concerning. Especially given projections that the $1T is likely to go up significantly over the next decade.

GDP is literally just in dollars as a unit

GDP is also an amalgam of various indicators of general economic activity: Consumption + Investment + Government Spending + (Exports - Imports). It might be all in dollars, but it is kinda like adding $X of Apples with $Y of Oranges.

Its good as a rough score to do relative comparisons between countries (and actually Debt/GDP is useful in that sense too), but as an absolute amount it doesn't mean all that much.

What matters is how much the debt servicing costs versus government revenues. Also how much that debt is growing (deficit) and/or what it would cost to reduce it.

But there's not much of a consensus around what is too much or too little.

I suppose 100% Debt/GDP is a good arbitrary number to raise the alarm, but it doesn't mean much on its own.

A quarterly debt to revenue ratio would be a lot more illuminating. There are very good reasons not to care if that ratio goes out of whack for one or two quarters. But any bro divergence that persists is bad.

This ratio isn't just better because the units match, you don't have to adjust the units for growth and inflation.

If someone has a debt it's entirely sensible to compare that to their yearly income, of course this tells you something. GDP is a proxy for potential yearly income in taxes for the government.

And now debt is 1 GDP year. I don’t see the problem.