You're getting confused.
You provided several links regarding
actual recalls. Specifically recalls for Abbott Molecular, Korvalab and Innova. The Abbott recall was in September 2021 for false positives. The Korvalab test was in June 2020 for false negatives. The Innova test isn't even a PCR test, it's a rapid antigen test. These have nothing to do with the ending of the CDC PCR test. They're just recalls because of quality issues.
The last link,
this one, is about the retirement of the CDC PCR test. It wasn't recalled. It was retired. The reason it was retired is because it wasn't needed. This was the first COVID test since there were no commercial options. Now there are many commercial options.
The tests couldn't distinguish between COVID and influenza because they didn't test for influenza AT ALL. They only recommend that labs switch to multiple tests because they're better. This is what the CDC said about it:
Does the CDC 2019 Novel Coronavirus (2019-nCoV) Real-Time RT-PCR Diagnostic Panel detect both SARS-CoV-2 (the virus that causes COVID-19) and influenza (flu)?
No. The CDC 2019 Novel Coronavirus (2019-nCoV) Real-Time RT-PCR Diagnostic Panel was specifically designed to
only detect SARS-CoV-2 viral genetic material. It does not detect influenza or differentiate between influenza and SARS-CoV-2. The presence of influenza viral genetic material within a specimen will not cause a false positive result.
There are other multianalyte tests available, including the CDC Influenza SARS-CoV-2 Multiplex Assay, that can simultaneously detect and differentiate Influenza A, Influenza B, and SARS-CoV-2.