You actually point down one of the key point of the model. This reaction releases energy, and this allows dark matter to stay in thermal equilibrium with a temperature different from the one of the cosmic soup. But this is maybe too detailed (or not enough)?
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I was just making sure that energy would still be conserved. I don't know, maybe things get weird with dark matter... I'm a dumb dumb on topics like this :)
Energy conservation is the basics. It is something very hard to give up, even for darker particles.