Earlier quoted context omitted.
While not wrong in itself, your comment epitomizes everything that has been wrong with our public health response. Trying to manipulate populations into a desired behavior by lying to them is, as you point out, counterproductive in the long run.
But it's not lying. If you have had COVID, you should still get the shot. The science is not close on this, the vaccine provides additional immunity in addition to what you get from catching COVID.
And while this pre-print [0] establishes that natural immunity is far stronger than vaccine-only immunity, the result is not conclusive for natural immunity + vaccine:
“Individuals who were previously infected with SARS-CoV-2 seem to gain additional protection from a subsequent single-dose vaccine regimen. Though this finding corresponds to previous reports, we could not demonstrate significance in our cohort.”
[0] https://www.medrxiv.org/content/10.1101/2021.08.24.21262415v...