Part of what I actually provided in answer to your earlier question at Why does binding energy cause mass defect? is below. What you say above does not address the major increase in kinetic energy which is due to decrease in rest mass (increase in binding energy). The above just addresses the part of the process before the actual nuclear reaction, and that is not responsible for most of the increase in kinetic energy. What you provide above is probably based on our lengthy follow-up discussions where you were asking about how the nuclei come together to fuse in the first place. Perhaps other responses can help explain this better.
Part of earlier response follows
Now, let’s consider a nuclear fusion reaction. Let the system be two nuclei that undergo an exothermic reaction: $ a + b -> c$ where $a$ and $b$ are the reactants and $c$ is the product of the reaction. That is, we “move up the curve of binding energy” in this reaction; the reaction increases the average binding energy per nucleon. We observe that the total kinetic energy of $c$ is greater than the total kinetic energy $a$ and $b$. From the macro viewpoint, no heat or work was added to the system (defined here as all the nuclei inside a system boundary) so according to thermodynamics the total internal energy of the system does not change. However, the kinetic energy of the products is greater than that of the reactants, so inside the system the
internal energy of the separate nuclei decreases to account for this increased kinetic energy. Before nuclear reactions were discovered and before Einstein, classical thermodynamics observed exothermic chemical reactions and attributed the required decrease in internal energy of the interacting constituents to “heat (or enthalpy) of formation”; for example, see one of the texts on ‘thermodynamics by Sonntag and Van Wylen. We now know that this classical “heat of formation” used to explain the decrease in internal energy of the constituents is a decrease in rest mass. So, for both a chemical and a nuclear exothermic reaction, the increase in kinetic energy of the products compared to the reactants is accompanied by a decrease in rest mass of the products compared to the reactants. For our fusion example, $c$ has less rest mass than the sum of the rest masses of $a$ and $b$.
For an exothermic nuclear reaction, once the reaction occurs the internal forces (nuclear and Coulombic) reconfigure the nucleons in an overall lower energy state. But, some initial kinetic energy of $a$ and $b$ is required to fuse since we are fusing charged particles and the Coulombic repulsion of the two positively charged nuclei must be overcome before $a$ and $b$ are sufficiently close for the short range strong nuclear force to become dominant. It is sort of like a ball on a high shelf would like to move to the ground due to gravity but some initial energy is required to bump the ball off the shelf.
For a fission reaction using a charge-neutral neutron, for some target nuclei- $235 U$ for example- a very low energy neutron can cause fission. But, you have to cause the free neutron to be released (e.g., from a previous fission) to be available to cause fission
The micro viewpoint for fusion (and fission) is addressed by details in models of nuclear binding mentioned earlier. These models propose explanations for why the binding energy of $c$ is greater than the sum of the binding energies of $a$ and $b$; that is, the nucleons are reconfigured in the reaction to be in overall less energetic states inside the nucleus, reflected on the macro scale as a decrease in internal energy and therefore a decrease in rest mass.
