There could be a reason that central bank do not write off their holding of government bonds: It will enforce the government to have some fiscal discipline just like any other enterprises
Government can buy 1 billion dollar worth of fireworks and fire them. There will be workers who make 1 billion dollar from the government order. Then those 1 billion dollar will flow to the society and cause inflation
But if government build 1 billion dollar worth of subways in the city. Then they will slowly take those dollars back through tickets sale, thus reduce the inflation pressure (Actually the rise of ticket prise is already an inflation, but that can be regarded as an increase in quality of life)
The whole point of debt based money issuing is to make sure the money will flow back through future consumption. But since there is interest, and consumption is usually less than income (long term wise), this scheme will just accumulate more and more debt that can not be paid back
Currently the government can only pay back the interest, when interest payment can not be sustained anymore, I guess central bank will have to write-off debt, or simply do not require an interest payment from the government (And that will not cause inflation, since no extra money are added to money supply)
In a normal soceity your right you pay for infrastructure and it pays for itself over time but most of the money printed went to bailouts from bad choices and to paying interest and warfare. War is very inflationary u blow up a bomb and thats it ur in instant debt. The us doesnt use its machines enough to warrant the money yet more is poured in to deter attackers and keep usd currency afloat.
Read up on the real housewives of wallstreet.. most of qe went to random joe blows like a bankers ex wife for business startup money for example. Why does she get that and others can starve? Feds books r closed and thats inflationary in itself.