Except that's not the issue for long-term immunity. Long-term immunity is about building an immune memory, which is dependent on which immune pathway is primarily activated while fighting off an infection. Research on other coronavirus infections has suggested that the part of the immune system required to build long-term immune memory is not strongly activated by infection, hence the waning immunity in a matter of months. You see this with other illnesses too: it explains why you need boosters for some vaccines when you're a child, or periodic boosters as an adult, and why vaccines are not a trivial thing to make (eg, why we can't just inject someone with the virus particles and call it a day).