It’s not that terrible compared to what’s out there and falls in the “trivial” category (which is not necessarily a negative; less complexity is good) but it’s far from ideal and it’d have to improve before pushing it globally.
As an example, some jurisdictions might declare individuals with single doses protected.
Another real example: the EU is unwilling to accept Covishield vaccinations, despite it being AstraZeneca/Vaxzevria manufactured in India.
I don't see this as any different than carrying around any other ID in my wallet. My driver's license also has my name and date of birth (plus information about my eyesight and home address).
The nice thing about the vaccination passport is that it is like a card in your wallet. There's no centralized server that's being queried. It's offline and distributed.