The key problem with this argument is that in order to acquire natural immunity, you need to contract the virus with all of the associated risks.
Vaccines allow you to acquire a level of immunity without the risk associated with infection. If you later become infected and recover, you will likely benefit from hybrid immunity for future exposures, but it would be illogical to willingly get infected just so that you could acquire additional immunity against that which you just willingly infected yourself with!
Studies generally show that naturally acquired and vaccine induced immunity are comparable, or that naturally acquired immunity is slightly superior to, or longer lasting than vaccine induced immunity.
Studies consistently show that having both (hybrid immunity) is superior. Note: "hybrid immunity" can also refer to the mixing of different vaccines, which has also been shown to be beneficial.
"The significantly lower rates of all-cause ED visits, hospitalizations, and mortality in the vaccinated highlight the real-world benefits of vaccination. The data raise questions about the wisdom of reliance on natural immunity when safe and effective vaccines are available."
This is a large population study (535,694 individuals) in Indiana.
"A statistically significant decreased risk (hazard ratio, 0.18 [95% CI, 0.15 to 0.20]) for reinfection was found among persons who were previously infected and then vaccinated versus those who were previously infected but remained unvaccinated."
"Among patients who had recovered from Covid-19, the receipt of at least one dose of the BNT162b2 vaccine was associated with a significantly lower risk of recurrent infection."
"Infection-acquired immunity waned after 1 year in unvaccinated participants but remained consistently higher than 90% in those who were subsequently vaccinated, even in persons infected more than 18 months previously."
"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."
"This study found that among Kentucky residents who were previously infected with SARS-CoV-2 in 2020, those who were unvaccinated against COVID-19 had significantly higher likelihood of reinfection during May and June 2021. This finding supports the CDC recommendation that all eligible persons be offered COVID-19 vaccination, regardless of previous SARS-CoV-2 infection status."
"Persons previously infected with SARS-CoV-2 gained additional protection against reinfection and COVID-19 from a subsequent single dose of the BNT162b2 vaccine."
"Our results demonstrate that Omicron infection enhances preexisting immunity elicited by vaccines but, on its own, may not confer broad protection against non-Omicron variants in unvaccinated individuals."