1) That CDC study has a relatively small sample size (N=738) and uses data from a single state during a 2-month period. The confidence interval on the "2.34" odds ratio is large (95% CI = 1.58–3.47). Most importantly, a tremendous amount of literature contradicts those findings. Nearly every large scale and long term serological study has demonstrated that immunity acquired through previous infection is at least equally effective as vaccination in preventing reinfection.

- 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. [1] (N=25,661)

- In conclusion, documented SARS-CoV-2 reinfections were exceedingly rare, with an incidence of 0.3 infections for every 1000 persons-week, and none were severe. Seroconversion after symptomatic or asymptomatic SARS-CoV-2 infection seems to be associated with a 10-fold reduction in risk of successive viral infection contamination, lasting at least 8 months. [2] (N=1,494)

- The study results suggest that reinfections are rare events and patients who have recovered from COVID-19 have a lower risk of reinfection. Natural immunity to SARS-CoV-2 appears to confer a protective effect for at least a year, which is similar to the protection reported in recent vaccine studies. [3] (N=15,075)

- Reinfection is rare in the young and international population of Qatar. Natural infection appears to elicit strong protection against reinfection with an efficacy ~95% for at least seven months. [4] (N=192,967)

- The degree of protection (10-fold) associated with seropositivity appears to be comparable to that observed in the initial reports of the efficacy of mRNA vaccines in large clinical trials.* [5] (N=3,257,478)

2) The preprint you cite is a "large community-based survey". I'll trade you pre-prints, this one is a retrospective observational study with data out of Israel [6]:

"This study demonstrated that natural immunity confers longer lasting and stronger protection against infection, symptomatic disease and hospitalization caused by the Delta variant of SARS-CoV-2, compared to the BNT162b2 two-dose vaccine-induced immunity. Individuals who were both previously infected with SARS-CoV-2 and given a single dose of the vaccine gained additional protection against the Delta variant."

3) Natural infection elicits antibodies that vaccination alone does not (for example nucelocapsid protein antibodies) [7]. The paper you cited does not provide evidence that vaccination on top of existing immunity confers any significant benefit to health outcomes in the face of viral mutation and variants of concern.

[1] 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/

[2] Risk of Reinfection After Seroconversion to Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2): A Population-based Propensity-score Matched Cohort Study https://academic.oup.com/cid/advance-article/doi/10.1093/cid...

[3] Assessment of SARS-CoV-2 Reinfection 1 Year After Primary Infection in a Population in Lombardy, Italy https://jamanetwork.com/journals/jamainternalmedicine/fullar...

[4] SARS-CoV-2 antibody-positivity protects against reinfection for at least seven months with 95% efficacy https://www.sciencedirect.com/science/article/pii/S258953702...

[5] Association of SARS-CoV-2 Seropositive Antibody Test With Risk of Future Infection https://jamanetwork.com/journals/jamainternalmedicine/fullar...

[6] Comparing SARS-CoV-2 natural immunity to vaccine-induced immunity: reinfections versus breakthrough infections
https://www.medrxiv.org/content/10.1101/2021.08.24.21262415v...

[7] Immunogenicity and crossreactivity of antibodies to the nucleocapsid protein of SARS-CoV-2: utility and limitations in seroprevalence and immunity studies
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7879156/