Secondly, sure, we don't know how long vaccine immunity will last, but that's a far cry from saying that vaccines were not designed for lasting immune reponses. For example, Pfizer/NTech's phase I/II trials explored over different doses, and they ended up selecting a dose of 30 micrograms rather 10 micrograms or 1 microgram because 30 micrograms elicited greater antibody responses, sustained over their measurement period of 43 days.[2]
Thirdly, quoting from the abstract of that same Nature paper: "Two doses of 1–50 μg of BNT162b1 elicited robust CD4+ and CD8+ T cell responses and strong antibody responses, with RBD-binding IgG concentrations clearly above those seen in serum from a cohort of individuals who had recovered from COVID-19." [2]
Let me state it again, without the jargon: Vaccinated patients had antibody responses clearly above those who had recovered from COVID-19. This, as I understand it, is why the CDC recommends that those who have recovered from COVID-19 still get the vaccine, as it offers extra protection from weaker or faded immune responses. [3]
Do you really think my statement that 'the vaccine is specifically designed to trigger strong and lasting immune responses' is wrong?
As I shared above, the phase I/II trials of these vaccines measured time series of immune responses to help select the dosing, and they picked a dose that had a strong immune response that lasted over their measurement time series.
[1] https://www.nejm.org/doi/full/10.1056/NEJMc2103916
[2] https://www.nature.com/articles/s41586-020-2814-7
[3] https://www.cdc.gov/coronavirus/2019-ncov/downloads/vaccines...
Last I remember reading, both are "for as long as it's been studied so far" - 8 months for natural immunity, 3 months for the vaccines. These numbers will increase as we continue keeping track of it to see how much the effect degrades over time.