I would take it a step further: the real problem is a lack of industrial policy to ensure that the EU has a good supply of home-made medicine. Such an industrial policy should at minimum include a medicine patent policy with the kind of clause Indian post-colonial patent policy had until the 90ies: if you don't produce in our territory we see no reason to hand out monopolies.

But preferably EU should go full delinkage: scrap patents for medicines, finance research from the public purse (grants and awards), and have competition in production. It was on the WHO agenda in 2014 and it had support including willingness to pitch in to research from the global South but it was shot down, mainly by the US.

In the current situation even pondering allowing generic production for vaccines that isn't delivered would probably scare Pharma enough to make EU a top priority.