For anyone unfamiliar, a job guarantee is a proposal of Modern Monetary Theory. Although the validity of MMT has neither been established nor disproven explicitly, it relies on, among other things, the ability of a nation to print its own currency, collect taxes in its own currency, and issue debt exclusively in its own currency. It is therefore not applicable in all nations.
> The ability to sell your labour to the central bank at the living wage, who then allocates it to local democracy to use as local democracy sees fit working for the public good.
How would a central bank determine allocations to various municipalities? This step necessarily requires discretion on the part of the central bank. Such a policy would distort the labor market, crowding out private sector employment and potentially producing malinvestment. It would also increase the power of the central bank, which is not necessarily desirable if the unelected nature of central bankers is a concern.
> the 'interest rate targeting' function of the central bank... is supposed to guarantee full employment
The Federal Reserve bank has a dual mandate of stable, low inflation and low unemployment. Central banks in many other countries are mandated only to maintain stable, low inflation.
> That it acts as a powerful targeted automatic stabiliser
There are other automatic stabilizers that can be implemented independent of the central bank. In the United States, for example, tax incentives for employer provided health insurance have a procyclical effect, as decreased employment during recession causing reduced healthcare expenditures.
> bank lending could never hope to match
Global lending has been distorted since 2008 due to the Federal Reserve's interest on excess reserves policy. The combination of increased reserve requirements, increased bank reserves due to the fed's enlarged balance sheet, and the availability of a risk free return on reserves has reduced the overall quantity of loans relative to prior trends. Even small, local banks, who would otherwise like to make loans and are subject to less stringent reserve requirements, have increased the reserves on hand due to the breakdown of the federal funds market caused by IOER. It's hard to definitively state that bank lending is less effective than other policy when it's been hampered by central bank policy for a decade.