They'd like to fire him? Where'd you get that from. In both the Mentalist and Elementary the deuteragonist and supportive cast love the protagonist. It's only when involving someone that doesn't understand the character that, that becomes a factor. Now if you want I can apply all of those things into each and every show featuring this "one special detective" as a foundation. Let's begin with The Mentalist and Elementary (obviously) then we have: Sherlock, Psych, Monk, Perception, White Collar, Castle, Lie to Me, Numb3rs and the list goes on. All of these build on the same foundation and thus carry similar features.
Some of them rely more on one aspect than maybe another one would like having a proper antagonist. Now it's fully possible to enjoy both The Mentalist and Elementary at the same time because they are quite different in their portrayals of their protagonists and stories, I should know, I do it on a weekly basis.