The Israeli preprint does, however, shed light on our increasing understanding of the potent immunity induced by getting the vaccine after having COVID – so-called hybrid immunity. Several studies show a substantial boost in both antibody and T-cell responses to vaccine in people with previous COVID infection.
Last years Israel study on Pfizer found the complete opposite of what you are saying. The rates of infection and hospitalisation did not drop off significantly until after a second dose was administered and then infection rates dropped off markedly.