Don't usually see that one much outside of Deviantart or FF.net

If it's impossible for your characters to act out of character, that means they don't HAVE a character. This not only makes it difficult for your readers to care about a bunch of interchangeable nobodies but removes the potential for character development over the course of the story. Your story will end up being purely events-driven, severely limiting your potential for storytelling as well as your readers' emotional investment.

If you really like the idea of your main character being shaken up by this particular case, why not come up with an in-character reason for it? What is it about this case that has him so upset/terrified? Maybe he doesn't even know and has to figure it out over the course of the story...and how to get over it so he can do his job. If you explore explore the why behind his actions, you could have a nice little personal story being told alongside the main events-driven story, or even influencing it. Instead of being someone who just reacts to outside events, your main character now has a stake in them, and we're rooting for him.

Whatever you end up doing, good luck.