You want to incentivise people to get positive COVID tests? Ballsy.
On a more serious note, I doubt anybody would be interested in enforcing this. Diners are going out of business due to COVID restrictions, and for many restaurant owners the choice between going out of business or looking the other way when people ask to be seated is clear. Furthermore the goal of all this is to keep the number of people who have contracted COVID as low as possible, your proposed ‘fix’ would only allow a small minority to work/participate.
I did recognize that there was an incentive in that direction. I think the question on that point is would this type of policy increase the behavior towards contracting the infection significantly more than currently exists over the benefits of a more open economy that takes some account of the fact some people are not at risk or a threat.
As you note yourself, incentives to defect, and so increase the spread, already exist. The approach I was musing about might offer a middle ground that perhaps counter intuitively actually increases the incentives to comply by producing a safe customer base. Would there be people tying to make their fake “I survived COVID and have (temporary) immunity IDs”? Yes. But it seems to me that with a legal option to operate on a limited scale under conditions that are actually safer than the current limited operations might just get the business to consider looking rather than looking the other way.
Also, broadening the focus towards who has recovered might support some better work place organizational aspect. For instance, if employers do have a growing number of staff that has been infected and recovered and now back at work (or could return to work) having the most at risk employees than have never been infected working in close proximity to the recovered workers and away from those who may become infected is probably a net good for that high risk person.
The point really is not about restaurants and diners but shifting some focus on we do have a large and growing group of recovered people who should pose no risk to others any time soon. The idea that we only have one population of people when looking at business activities and what can and cannot be open, at some point, becomes rather stupid and actually increases the average level of risk compared to what could be achieved I think.