Why do you just ignore the fact that for everyone to get the "natural immunity" requires millions to die first?
Unvaccinated people have to risk death to get your "better protection". For vaccinated people, best case scenario is that they're completely protected and worse case scenario is they get sick but almost certainly won't die and now they DO have the natural immunity on top of vaccine protection.
You're comparing the SECOND time that unvaccinated people get sick to the FIRST time that vaccinated people get sick while completely ignoring the consequences of that first illness in the unvaccinated.
Notice you're also ignoring the bottom of your own link:
Dr. William Hanage, an associate professor of epidemiology at Harvard’s T.H. Chan School of Public Health, said that it is “impossible” to know whether the COVID vaccine or natural immunity is more protective against the virus due to the lack of knowledge regarding the level of protection natural immunity gives a person over time. Reinfection occurs in about 10% of people after having contracted the virus as a result of a decrease in immunity overtime.