Convalescent people do have a more diverse immune response, to other parts of the virus. And after a vaccine actually have even stronger responses still.
The immune response to covid and the spike protein in immunized people is very uniform and the antibodies we produce are very similar (although not identical.)
But the specificity of the spike targeting was chosen for a reason, it is VERY unlikely there is another spike protein that will work as well and entirely evade the immune system. Studies have been done and threatening spike mutations have been checked, and it doesn't seem like there are good alternatives.