Er while each country has been trying to defend its own interests especially in the first days,, they still coordinated through EU. Also the ECB was the first to act for the benefit of all, injecting 750 billions € to support the economy, and announcing 120 more billions for loans to small companies hit by the crisis. And Van der Leyen has been very critical of the initial lack of cooperation and especially the mask production hoarding (which led to deals to share a bit more in the end). All of it in addition to any help that each country will devote to the crisis, for which Brussels also stated that they removed all budgetary constraint.
The main problem is there's no centralized authority for health management, it's something that each country wanted to keep under its "sovereignty", like army. And guess what, now we realize it would have been a good idea after all.
Nobody cared about the EU for the first few weeks and only after they started to shit with bonds which basically means cull all wealthy nations of there money to transfer it over to the south with massive loans ( aka north pays for the south ) which are already bankrupt anyway and make everybody poor was never something anybody cared for in the north.
Bonds where a wet dream of brussel to push so they could bankroll the south and lock the north into EU forever because they now have massive dept and far less money to deal with. Because the south can't even pay for there own shit. Let alone the east. What's the point to sit for nothern wealthy country's in a EU that doesn't make them money? but kills there country's? fucking useless.
Why would Brussel want this? power, to keep the EU dream afloat and feed there pet company's they get rich from with massive money injections. it's there green dream 2.0.
If you think that tiny 750b is going to help anybody but those corrupt shits in brussel to feed their pet companies to make themselves ultra rich, u are just kidding yourself. South has never been able to deal with money and that's the end result of it, NL will probably dive already 200b into more dept and that's a rich country with corona virus based on 17m people, good luck with 500+m more with your 750b its nothing. Its straight up wealth transfer.
Your universal healthcare and military also has problems.
1) northern country's can pay for the southern country's and destroy their own healthcare systems while they are at it and go waaaaaay back into time which nobody in the north would ever vote for. Healthcare in the north was already hitting critical levels by itself, now imagine them bankrolling the same shit for far less wealth country's? or we also going to loan endlessly on again the same country's backs to pay for it? sounds great, aka not doable.
2) one military under one flag, which never be accepted by any country for obvious reasons such as hitler 2.0 and people do not remotely relate themselves in anyway towards the EU to make this happen. Also conflicts will rise as those shitters in brussel will exploit it the moment they can which nobody in the EU even remotely wants.. If dutch would sign for example for militairy pack under one flag, the militairy would be dead the next day because everybody would leave, now imagine other country's that are far more nationalistic.
Nobody trusts eachother even remotely enough to do this and never will. And that's good because its a very fucking bad idea to give brussel any militairy might. These loons will start to use it on everything that's against them with england probably there main target to teach them a lesson.