When calls are made for a central bank to play the role of “lender of last resort” in government bond markets, such calls effectively amount to the central bank being asked to directly fund illiquid sovereigns, either via direct interventions on the primary market or by extending direct credit lines.
Such activities are not legally within the reach of the ECB, since the Treaty clearly imposes the prohibition of monetary financing (Article 123 TFEU). There must not be any circumvention to this prohibition. Again, this Treaty provision was not chosen arbitrarily.