It sort of looks from the outside that Brexit was done just in time as the UK government is now saving more UK lives than they would otherwise. If I were an EU member I would be extremely critical of the current regime and truly question how they are legit when the EU is far behind the rest of the developed world in this.
It’s not fair to EU citizens that pay into the pot of mostly unelected representation.
What can we say? Once upon a time there was a belief that the world could come together and solve it problems if there just was some good will among the countries of the world.
This spirit still survives in the EU leadership that have spent so much time working for that on the European scale, so they simply have too much faith in international collaboration.
So, if everyone had brought in export bans, then it's likely that wouldn't have been the end of it; trade restrictions on precursors and equipment and those little glass bottles (these were seriously a problem for vaccine manufacture at one point) would have followed, and world production would have ground to a halt. No country/bloc except possibly China can make a vaccine in large quantities single-handed.
The EU's mistake was in being the only big producer not to ban or heavily restrict export; being the last one to do it would be very dangerous and more likely to cause escalation. That's still a concern for current proposed EU export restrictions.