50% is the same as random chance. In other words, this 99% specificity test can do no better than a coin flip when declaring a positive result. So screening in this scenario is not warranted because data that is no better than a coin flip is not data — it’s random chance.
However, the situation is much worse than this because neither PCR nor antigen tests are close to a 99% specificity level in practice, for various reasons (Braunstein et al. 2021). Lee 2020 performed a lab analysis of the CDC PCR test accuracy, which was widely used in the first months of the pandemic, and found it had a 70% specificity (i.e. 30% false positives) and 80% sensitivity (20% false negatives). This level of inaccuracy matches the CDC’s own internal report that found 33% false results when its PCR test was released in late February 2020, as reported on by National Public Radio (Temple-Raston 2020).