The crossover has already been done to death.
But I wanted to try a different style, plus John is fun to put in different jumpers. I like the idea of Whovian John.
(John is acting like I do; nobody in the house is allowed to talk/make any disruptive noises when I am watching Doctor Who).
Also they moved the furniture.
Sherlock, John, and TARDIS are BBC and their respective creators.