EU has not shown itself to be able to do Vaccine roll out quickly. Spain for example is run by PSOE/Podemos left government.
On lock downs. In Madrid police were going around strictly enforcing lock down.
In this country there was not full lock down. Also I don't think in this country it would have worked. People will to some extent follow government rules but not all the time.
I also think how different governments across Europe will deal with the post pandemic period is going to be where political differences will emerge.
Here it could be some form of austerity again. Other European countries, within constraints of being in EU /Euro, might do things differently.
Bit of a different view from Larry Elliot in a guardian article I read few months ago.
Centralised approach was meant to underline Europe’s solidarity but has had opposite effect
www.theguardian.com
The failure of EU to organise a Vaccine roll out is example of where not being in EU has meant a national government has been able to just get on with it.