The premise of the show is gold, it's the main reason I stuck with the show. True, it is very unlikely that there could ever be a forensic analyst who murders the bad guys in his spare time. I get that, by the same token what are the chances that a down-on-his-luck cancer-stricken chemistry teacher will become a meth kingpin and become the biggest drug lord on the planet? Both are very unlikely.
Knowing this does not mean that I forget about the execution and put my brain in a coma as I watch each show. Based on your line of thinking, a fictional story shouldn't give a crap about the execution, because after all, it is fictional.