I can see why Rhythm Thief went somewhat unnoticed back when it launched, years ago. For starters, it has that sort of Layton-style appeal to a market that the 3DS could never quite capture. The story and characters is really nothing to write home about either.
It has literally all of the tropes of the thief genre: the lovable rogue, the private detective, the workaholic inspector, etc. And unfortunately it takes the worst part of the Layton franchise as well, which is the “touch everywhere” syndrome.
Where the game scores a victory is in the minigames, which present quite a challenge and are worth playing through again and again to get a better score. However, the exploration parts are weak, so as a whole the game might not be enough to recommend. But it should be easier to find cheap today, which would make it a much easier purchase.
On the bright side, it received a port on iOS some time ago, so it still got more attention than Doctor Lautrec ever did.