The country of destination issue visas, not the country of passport origin.
There are seven main problems I see with such Vaccination passports:
A vaccination does not prove a lack of infection. They won't care, it's about risk management not eradication
A vaccination may not protect against any new variant. They won't care, it's about risk management not eradication
The passport has a very limited life. They won't care, it's about risk management not eradication
The cost of setting up and implementing such a scheme would not be borne by the government, so individual participants would be financing the scheme.They won't care, it's about risk management not eradication
It does create a discriminatory effect, those that can afford it benefit, those that cannot afford it are discriminated against. They won't care, it's about risk management not eradication
The passport always has the option of being exploited for other 'governmental' reasons. They won't care, it's about risk management not eradication
Any database can be exploited for nefarious activity. They won't care, it's about risk management not eradication