This might be a silly question. I've always assumed that the neutron had a binding energy of 0 because it's only one nucleon that isn't interacting with any others most of the time, just like a proton. But I haven't been able to find any sources that confirm this.
And to be clear, I'm not talking about talking about binding energy, as in the energy required to separate all of the nucleons in a nucleus, not mass defect.
The "binding energy" is the energy that has to be supplied to disassemble a bound system into its constituent parts. When thermal (milli-eV) neutrons capture on hydrogen, each capture releases a 2.2 mega-eV photon. That energy is the binding energy of deuterium, and hitting deuterium with more than 2.2 MeV allows it to dissociate into free nucleons again.
The nucleon is the ground state of QCD: you can't disassemble a nucleon into lower-mass constituents. (If you hit a nucleon hard enough to make QCD things happen, you can produce a heavier baryon. It is sometimes helpful to imagine the $\Delta$ baryons as bound states of nucleons and pions — but other times that picture is not useful.) So the most reasonable value for the "binding energy" of a free nucleon is zero, just like the "binding energy" of a free electron is zero.
While the free neutron does decay to a proton, an electron, and an antineutrino, the neutron is never a bound state of its weak decay products. Binding energy is the wrong tool to describe that problem. The free neutron and the free proton both have different, nonzero mass excess (a.k.a. mass defect), which is closely related to the binding energy in nuclei with $A>1$.
Individual things don't really have a binding energy. It's the system as a whole that does. Further, we're really only interested in the differences of these energies. Any zero reference is driven by convenience. This is true for gravitational energy, chemical energy, nuclear energy, etc.
If our (nuclear) system is just a single nucleon, there is no way to manipulate the system into a different nuclear configuration. With no differences in state, there is no energy difference. Saying that there is a specific "energy" associated with this state doesn't seem to be well defined.
If our system is a pair of nucleons, we can say that the energies of the bound state and the separated states are different. This difference is referred to as the binding energy. Often it is useful to ascribe a value of zero to the separated state, but that is arbitrary.
