How can countries afford to run budget deficits for decades on end and not become overburdened by interest payments on those debts?
Because they have low interest rates and growing tax revenue.
As long as your income is growing faster than your debt, you can keep borrowing.
Simple : inflation.
The model of create deficit budget to enact infrastructure to increase production that lead to higher tax collection to offset the deficit doesn't hold.
Because there is no guarantee of return (no mater how long the term are). There is government that enacting infrastructure/spending on the wrong place. Corruption, grafting are norm in all government institution.
By slowly supply more money into the system, it will dilute the value of interest served. And this the reason of why some country bonds are deems "junks", due to the inflation factor.
If the production able to absorb the additional money(where people buy goods and services instead of hoarding it), then you will not see goods price increase.
"Income growth" are ambiguous term. It is relative to inflation level. Imagine a country print trillions of notes and give them 10,000 to every of them, does this denote "income growth" or worst "GDP growth" ?(also imagine this money are given to cronies)
One of the cheeky but "morally correct" inflation are once play by Japan bureaucrat during the first few year after GHQ occupation (1945-49). Where the government run a huge deficit due to fix payment to thousands of high ranking feudal class family. Since civilian doesn't hold much wealth, bureaucrat purposely create a superinflation.
Let me elaborate how : (all number are not actual historical figures) Before the super inflation, the bureaucrat need to pay 360 millions yens(say 1 US dollar = 360 yen). After enacting the super inflation, it devalue the money (say 1 US dollar = 360,000 yen). So the 360 mil yens suddenly become the original 1/1000. So the deficit government only need to enact 1/1000, deficit fixed. Since post WW2 Japan doesn't have much cast on hand, they will collect wages according to inflation adjustment, thus they are not affected by the problem at all.
This is a NOT repeatable method. Not unless you countries are raze to a flat land to play such card. Since people in most country today held significant number of cash today. This method will destroy the trust on cash, also it will destroy the foreign trade value of your currency. During 1945-49, Japan doesn't have much trade with any country.