Unfortunately, vaccine passports appear to be used more as a punishment for not complying than being about disease control.
Edit - Incredible how you can be downvoted for laying out crystal clear logic there. Covid, eh!
It would not be efficient for the immune system to keep antibodies circulating in large numbers for every pathogen you've ever been exposed to. Instead, the immune system generates longer-lasting memory T and B cells, which allow it to recognize pathogens it has been exposed to in the past and more quickly produce antibodies to fight them if necessary.
Most individuals who have been vaccinated or recovered from infection will have protection against SARS-CoV-2 even after the antibodies produced immediately following vaccination or infection have waned and become undetectable.
The evidence to date suggests that the long-lasting memory T and B cell responses are stronger and broader in individuals who have recovered from natural infection, while those who have been vaccinated have higher levels of neutralizing antibodies that wane quickly.
Ultimately, whether you're talking about vaccination or natural infection, the problem with your statement "the test to accurately measure that the people indeed have the antibodies in sufficient strength" is that there is no such test because there is no validated model to correlate titers of neutralizing antibodies to protection against infection and illness.
Let them pay for it, and make its validity valid for only as long as that rest is predictive. If they can’t get it due to distribution issues, they can do the same thing people who refuse their standard vaccines do—stay away from (and be let be by) others.
The goal is to control the disease, not the people.