The benefit of this system is that at least we have a unified document right now. From what I've heard, covid recovery is indeed part of the QR code so any country accepting half vaccinated people that have recovered doesn't need to deal with different paperwork from every member state.

The lack of getting people a second shot is disappointing, but with the limited availability of vaccines it's understandable from a health perspective. The goal of vaccination isn't to help people travel, it's to prevent a deadly disease, after all.

We'd be better off with a common deciding factor what measures are acceptable to cross the borders, but areas with tourist-centric economies are incentivised to reduce the access requirements, and other countries are paying for those economies while they're still failing, so health and safety wouldn't be the main concern of such a common approach. The national approach doesn't have this problem, at least not for the countries supplying the tourists.