Sherlock Holmes may be a rationalist, but his process is invisible to the reader.

A typical Holmes conversation (in form, at least):

Lestrade walks in.
SH: From your appearance, I can tell you just came from the morgue.
L: Gadzooks. You are correct. How did you know?
SH: I smell (some chemical) on your clothes. Also, the leather in your shoes is discolored as if (some other chemical) has dripped on it. The only places that use those two chemicals are (some ridiculous industrial location) and the morgue. Since you are a police officer, the logical conclusion is that you have just left the morgue.

But all Holmes' facts (except that Lestrade is a police officer) are invisible to the reader. Also invisible to the reader are the facts about Lestrade that are irrelevant to the story or the analysis (i.e. Lestrade was wearing a brown jacket, he recently shaved, and is carrying a note in his pocket, probably a list of items his wife wants him to buy on the way home).

Even if we wanted to, we couldn't follow along with Holmes' reasoning, including the dismissal of the irrelevant facts. In short, Holmes' "rationality" is really deus ex machina in favor of a character in a story.