You don't think that police officers wouldn't be interested in studying the legendary powers of the bushi? Now available from this short mean guy who is staying up at the ryokan on the hill there, at a ten-day seminar for the low low price of only three yen per student? You, too can restrain your suspects with the powers of Minamoto Yoshitsune himself, handed down through the fearless Takeda clan of Aizu domain! Learn the secret power that will allow to lift any man - even GERMANS! - who grab your wrist! To immobiliza multiple attackers with the press of one finger! To immediately sense an attack from behind and instantly neutralize it!
The police were modernizing all over the country around these times, right? You don't think studying with the old jujutsu guy was kind of folksy for professional law enforcement?
The police already trained various budo. Such training is, and was, required for them. The police dojo were one of the big venues for keeping training going during the Meiji era once the samurai class was disbanded and the professional budo instructors became unemployed.
Frankly, the fact the Takeda didn't get a permanent job from any of the bigger city police departments is kind of suspicious. Those departments needed lots of ongoing instruction, and if Takeda was really as awesome as the stories claim, surely one of the departments would have taken him on. Japanese police are extremely practical that way.