The energy of neutrons isn't really analogous to the energy of atoms in chemical reactions, but absolutely affects the reaction dynamics. The "cross section", or interaction probability, is a strong function of neutron speed. In bombs the neutrons don't get a chance to slow down, but in reactors you try to reduce them to "room temperature" speeds using collisions with light, inert nuclei (the moderator). Here's a diagram showing the interaction probability vs. neutron speed for a few isotopes of uranium: https://tinyurl.com/u235-cross-section

It changes very little because there’s nothing to receive their kinetic energy.

Neutrons lose energy by colliding with things of similar mass, such as hydrogen nuclei (often in water). If they collide with a heavy nucleus, such as plutonium, they just bounce off without losing speed. (Or fission or capture.)

Think of billiards. The cue ball may slow or stop after hitting another ball, since they have similar masses. But hit the rail and it just bounces off, at the same speed, because the table is so much heavier.

If there are no light nuclei in the environment, then the neutrons won’t slow down.