As they should. Why would you expect domestic citizens being deprioritized?
An export ban would have made hardly any difference as production would have probably been aligned around the fact.
The EU is not 'naive' - it is 'failing' perhaps the most important test since it's inception.
Being a 'few months behind' US/UK/China etc. will mostly ok, but if it's more than 6 months behind, then this failure will resonate for decades.
Fair or not fair, right or wrong, the facts will be immaterial to the headlines that will ring for a very, very long time.
For example Denmark is doing quite well, but Bulgaria is doing quite bad.
So to repeat, healthcare is not a responsibility of the EU.
The EU is definitely the entity responsible for acquiring the vaccines on behalf of nation states - this is what is failing.
The 'delay' is not due to Denmark inability to field nurses, it's in the EU's ability to secure product - for whatever reason.
And in the end, it won't matter. If the EU ends up 6 months behind other nations 'there will be no excuses'.
I think that they'll probably catch up, but there's a real possibility they don't.
Why? This isn't something the EU normally does.
The approach actually makes sense, if everyone was acting rationally and competently it would work.
But they screwed it up.
Everyone is clamouring about the 'new world order' and 'pivot to Asia' and wondering what the 'Brexit' result would be ... and the optics of this are 'EU in last place'. It's just a bad look, and it's an event that will ring through time with long lasting effects, at least in 'hearts and minds'. There's still chance to catch up however.
USA never intended to export vaccines under Trump administration, Biden is upholding it.
The only difference really is that our EU politicians had big words, but when the rubber hit the read went the same route as everyone else.
To be honest, EU politicians were naive.
We should have banned all exports very early on as everyone else did and then graciously allow exports on case by case basis to the level we have now.
It would have been a lot better optics, but the same practical outcome.