Perhaps. It depends on how easy it is to adapt to the metric, how risky, and how much upside there is. It's kinda like antibiotics. Use them too often and the pathogen adapts. It would be an approach that would have to be balanced with others.
For what it's worth I do think it is very silly to announce you are using metrics like this. Ideally you'd not want people to know what tipped you off that they were just cashing checks. You would fire them gradually over several weeks or months, and explain it some way that doesn't easily point back to the filter metrics. This approach of announcing it is like exposing pathogens to a sub-curative dose of medicine.
Anyway, I don't get the sense from the other commenters that the main concern is for the wellbeing of the company -- that they might be at risk of being gamed. I don't think an employee should have an expectation of privacy in at least several of the spaces used in the article as a signal, if any.
