Governments certainly could spend money into existence like that. Unfortunately they are under the influence of the banking system. As it is, everyone believes that new money must be created as debt and everything else (including Bitcoin) is evil.

That said, creating $1,000 per nose and month would certainly debase the money even faster than the ECB and the FED is doing it now. But a smaller amount, say, $100 per nose of debt free money would IMHO do much more good than those $100 by getting things going again.

[EDIT] I should make it clear that YOU exist for the benefit of the fiscal financial complex, not the other way round. So it should be clear that your idea is completely counter productive as it would set you free from wage slavery. The system wants you to be indebted. Submit to it.