If the ECB has to resume quantitative easing, should it not buy only private financial assets?

It is possible that the ECB may have to resume quantitative easing in the future, should the euro-zone economy weaken. Unlike what it has done in the past, would it not be better if the ECB bought not government bonds but only private financial assets such as ABS, corporate bonds and equities? This would give it a direct influence over companies’ borrowing costs, without giving rise to the moral hazard linked to government bond purchases, which encourage some governments to run up excessive public debt .