This points to why the EU will likely disintegrate - member countries can't print to monetize country debt. Either EU members split out to regain currency autonomy, or EU officially federalizes member country debt.
Obviously the latter will happen - it is in fact already happening, between eurobonds and recovery fund. We just don't make a big song and dance about it - quiet work is how the EU is managing to do the unthinkable of federating this anarchic and unruly continent.
The economic imbalances between EU states are nothing, compared to the ones between US states. Do you see the US "disintegrating" anytime soon?
I could see Illinois imploding due to retiree obligations and pieces of Illinois being absorbed by neighbor States. More likely for federal government to take over State pensions because federal government can emit unbacked money.