A few things of note:
- The (residual) strong force isn’t really that complicated; it’s strongly repulsive at short range, then there’s a dip at ~1 fm where it’s strongly attractive, then it rapidly falls off to zero as you get to 2 fm and above. This graph is for protons but it’s similar for any two nucleons.
- The Coulomb repulsion is never insignificant at typical nucleon distances. Even compared to the peak of strong force attraction, it’s still around 15% of the strength. And it quickly becomes dominant a little farther out.
- Nevertheless, there is an equilibrium position (actually two but the second is unstable) between two protons. So there must be another decay mode in that case, or else tunneling (Wikipedia says that a small portion of 2He decays to deuterium, but mostly it’s proton emission. I guess it’s tunneling, then)
So why does the Coulomb force break apart nuclei as you get to get to larger numbers? Well, the strong force repulsion at close range means that the nucleons can’t pack together too closely. But that means that as you add more nucleons, some of them will necessarily be farther apart than if you just had a few. You can pack 4 oranges together so that each touches the other, but with 5 that’s no longer true. One pair is farther apart; nearly double that of touching pairs. Which puts it into the quickly decaying territory of the strong force. A 1/r^2 force on the other hand still has >1/4 the strength.