While it might be fair to challenge the credibility of WSJ, you should know that the CDC study you cited had a relatively small sample size and was limited to a small geographic area over a 2 month period. Recent large scale multicentre studies with ~100x more participants have provided strong counter evidence that natural infection confers highly effective protection [3].

> A previous history of SARS-CoV-2 infection was associated with an 84% lower risk of infection, with median protective effect observed 7 months following primary infection. This time period is the minimum probable effect because seroconversions were not included. This study shows that previous infection with SARS-CoV-2 induces effective immunity to future infections in most individuals. [3]

For reference here's high quality publications supporting GP's claim that natural infection provides robust and durable immunity that is at least as protective as vaccination [1][2][3][4].

[1] SARS-CoV-2 infection induces long-lived bone marrow plasma cells in humans https://www.nature.com/articles/s41586-021-03647-4.pdf

[2] Longitudinal analysis shows durable and broad immune memory after SARS-CoV-2 infection with persisting antibody responses and memory B and T cells https://www.cell.com/cell-reports-medicine/fulltext/S2666-37...

[3] SARS-CoV-2 infection rates of antibody-positive compared with antibody-negative health-care workers in England: a large, multicentre, prospective cohort study (SIREN) https://pubmed.ncbi.nlm.nih.gov/33844963/

[4] Necessity of COVID-19 vaccination in previously infected individuals https://www.medrxiv.org/content/10.1101/2021.06.01.21258176v...