Kabukichou Sherlock gets a lot of criticism for being a lackluster comedy based around the character of an off brand Sherlock Holmes, but as the show goes on and on it gets more serious, emotional, and tense. The first half is primarily light hearted and comedy heavy to set the tone of how things 'should be'; but turns away from that halfway into the Jack the Ripper case, which the case and the events that are around it become the main plot of the show. The show has plot twists that some might see coming, some not, depending on if you know the Sherlock Homes books and whether you think its going to follow the books at all.
The gimmicky inclusion of rakugo is also an issue of contention with watchers, as it is gimmicky and one of the things that is there explicitly to make the show distinct. That said the rakugo has explicit reasons for being there, this Sherlock loves roakugo but didnt have enough talent for it but in his depression after realizing this was convinced that if he loved it so much then he could apply it to how he acts in his life- detective rakugo. But utmost Sherlock performs it because he wants to and finds it fun, not because he hast to as part of his gimmick. As such the rakugo fades off during the darker second half of the show. Its a great emotional anime by the end that explores all of its characters on a psychological level by the end.
This was my second review for the show after completing it, here is my original review after only watching the first half watching the show:
Less of a Sherlock Holmes story and more of a weird cross between Akechi Kogorō
and his Boy Detectives Club meets Sherlock Holmes, where the character of
Sherlock is part Holmes and part Akechi, and his 'partner' is part Kobayashi and
part Watson.
Each episodic episode is enjoyable in its own right with events and outcomes
logically making sense. Possibly the largest oddity that adds to the show is that the
mystery reveal at the end is done though rakugo as apposed to just exposition.
The show is interesting for its mashup of characters and ideas, its not the most
fleshed out but entertaining non the less if you enjoy the characters. That said the
show doesn't do any particularly knew of interesting, but what it does is well
executed for what the show intended to be.