Wouldn't an unspent, untaxed amount of money also come back to the government as private individuals spent it? Your model assumes that tax revenue is coming from a sector of the economy with low velocity of money.

I have heard this suggestion before in the context of overcoming suboptimal risk intolerance (like right after a crash) but for it to work you would have to derive the tax revenue somehow from people who were not spending money. That's one thing I've never understood about Keynesianism.