nuclear physics - Why don't neutrons cluster on their own?

"The answer lies in their one part in a thousand extra mass. Adding neutrons costs a little in mass, and in Einstein $E=mc^2$ implies that mass equates to energy. So it costs energy to add neutrons(due to their mass) and it costs energy to add protons(due to their electrical repulsion). This qualitatively explains why the elements have N larger than P, but not by too much.

This extra energy locked into the neutron's mass also leads to instability. As nature seeks the state of lowest energy, like water running downhill to sea level, so a neutron left to itself will eventually experience beta decay: $n\to p+e+\nu$, which converts it to the marginally lighter proton, the excess energy being transformed into the electron and neutrino. So while a neutron in a nucleus can be stabilised, if you gather too many together, they will undergo beta decay, increasing the number of protons at the expense of neutrons. Conversely trying to put too many protons together and their net electrostatic repulsion destabilises them; in this case it is possible to lower the net energy by "inverse beta decay" where one of the protons converts to a neutron: $$ \rm p\text{ (in nucleus)} \to n \text{ (in nucleus)} + \text{positron} + \nu. $$ The net effect is when collections of N and P get too big a mismatch, beta decay or inverse beta decay moves the whole back toward the "valley of stability" where the number of neutrons N tends to exceed the number of protons P."

(The above is from a book called "Cosmic onion. Quarks and the nature of universe")

From my understanding (not too sure as I am new on this), it took much more energy to gather protons together as compared to gathering neutrons together. What holds them together is the strong force and since the strong force holding them together is the same, there will be "a lot of strong force" left over when holding just neutrons together. As nature seeks to minimise the energy state of the nucleons, some of the neutrons will decay to proton such that there will not be "any strong force left over", hence ensuring that the energy state of the necleons are minimise. If what I say above is true, the neutron and proton "produce" equal amount of force carrier particles as is it because they themselves are made of quarks held together by the same colour charge and thus each of them produce the same amount of residual strong force?