Can someone explain why heavy nuclei prefer to go through $\alpha$-particle decay instead of nucleon decay?
Nuclei are quantum mechanical "particles" composed out of protons and neutrons, which themselves are composed out of quarks and a sea of gluons and antiquarks. The basic holding "force" of this is the strong interaction force, modeled with QCD for the protons and neutrons, and a spill over force from the protons and neutrons called the strong nuclear force.
Quantum mechanical models have been developed which explain the decay and fission behavior of nuclei.
Hand waving: the alpha particle is very tightly bound, as seen in this binding energy curve, and in addition, it is stable. Thus within the "bag" containing the nucleons a stable configuration of alphas can exist in unstable nuclei, and the fission or decay into alphas may be energetically favored over the emission of a single nucleon, for a particular nucleus.
The models fit this behavior and can predict how other nuclei will fission or decay.