That’s what Dr Fauci said for seasonal flu in 2004.
Yes you will have antibodies from being exposed to one strain of flu. You won’t for the next strain.
Catching COVID carried a far greater risk because although symptoms can be mild in many cases it can kill vulnerable people and it spreads incredibly quickly. At the peak of the pandemic, hospitals were being overrun by people sick with the virus, which affected everyone’s access to care. Vaccines helped prevent the spread of new strains to vulnerable people and reduced pressure on the hospitals.