Least of all the EU?
Criticize EU all you want, but the most effective EU country is (I believe) 6th. Sure, that's way behind Israel and UAE (don't get me wrong, I would have love to see us at the same pace).
And really, the EU doesn't have much to do with it any longer. They made sure that EU could buy plenty, following the demands from the nations (of who plenty cared much about costs). Now that we're getting them, it's mainly between the suppliers and the individual nations.
Right now the main worries are that both Pfizer/Biontech and Astrazeneca are struggling to deliver what they've promised.
And BTW, initial reports are that nothing is really wrong with those vaccines in Sweden. They were transported at a too low temperature (more like the temperatures for the Pfizer vaccines), but they don't expect to be needing another vaccine for the 1000. Some other vaccines with the same problem are held back though.