I like your analysis but think it is too narrowly-focused. It's true that government doesn't invest as efficiently as the private sector, but that's not the macro picture. Nor are we likely to see a recover via private debt.
Debt efficiency has been declining over time if you combine public and private debt. The government ramped up spending because the private credit market was contracting. The total debt growth is exponential, and it's about out of gas.
While the debt efficiency has been declining, interest rates have been going down. Now they can't go much lower. I don't know how long we can stay stagnant, but there is currently no way to go "up" from more debt.
Yes, the government debt was a last push to prop up the GDP. But whether private or public debt, if it is out of gas at near-ZIRP, it's really out of gas.
Just maybe it's time we realized that debt and spending don't replace productivity. They simply borrow from future productivity. When you don't pay the accordingly market interest rate for that borrowing, you will pay for it later.