And then immediately on the addition of a hydrogen, the resulting nucleus is suddenly in a higher-energy (lower binding energy) state than some non-hydrogen spl

And then immediately on the addition of a hydrogen, the resulting nucleus is suddenly in a higher-energy (lower binding energy) state than some non-hydrogen splitting of it. And since most of the results of hydrogen hitting something are unstable, this happens almost immediately, leaving the total process looking more like fission (a proton hitting a nucleus, and producing two nuclei of smaller mass than the original). Which is, in fact, how uranium fission works, only with neutrons rather than protons.