Why does K have a greater electron affinity than Ca?
Neither K nor Ca "wants" to ionize.  Both ionization energies are endothermic.  This question refers to eelctron affinity, which is gaining an electron.

K has a more exothermic electron affinity because the electron gained fills the 4s orbital.  In Ca the electron goes to 3d.  The energy gap between 4s and 3d is enough to make the process barely exothermic.

Note that the numbers given in tables are positive but that the process is exothermic.