"Let's ask a slightly different question. Why do governments pay interest on their debt? Actually, it sounds like a different question, but it's really the same question. Why finance government deficits with interest-paying debt, when you could use non-interest-paying currency?
The answer is the same: you pay interest on the debt to encourage people to hold it and stop people spending it. If you cut the interest rate on government debt, will people sell it back to the government for money, spend the money, and cause inflation? If not, then Aggregate Demand is too low, and the problem is deflation, not inflation. So there's a free lunch from cutting the interest rate on government debt. And the government should eat that free lunch. And then the Long Run Government Budget Constraint kicks in again".