The best evidence we have thus far shows that antibodies, at least in the numbers required to prevent active infection, only last a few months. So, say you got infected in March, antibody testing today likely would not show that, nor would it provide lasting protection from infection. If you don't have antibodies, you're not 'safe' from infection. It might give people a false sense of security, though, and end up compounding the problem. I do think antibody testing is a good idea simply to get a grip on the reasonably current prevalence in a given community which could be used to guide mitigating interventions.

I don't think it is clear that having antibodies equates to 'cured'.
How many have some long-term (ongoing ? ) damage ?

Interesting article. One report that I read said 3 months was the max for the antibodies post infection. So, unlike things like chicken pox or measles, the antibodies aren't permanent. This is a challenging virus.

Interesting, but I will stay with social distancing, mask-wearing in public, and a vaccine once it becomes available. That strategy seem to work for New Zealand, Germany and another countries with a more disciplined population.