This makes a lot of unfounded assumptions about what the police can and would do. There's not a lot the police can do after a bike is stolen within proportion to the value of the stolen bike and bikes are both easy to steal and easy to scrap for parts (that are practically untraceable in most cases). So what do you end up with? More police patrols in "high crime" neighborhoods and more "spot checks" (a la stop and frisk), both approaches that have been demonstrative failures for decades but satisfy the political pressure to "do something".
A better long-term solution would be to reduce the need for policing by mending the socioeconomic conditions that result in bike theft. Rampant bike theft isn't a global issue and is actually less of an issue in some countries that have a lot more bikes on the streets per person than any city in the US does. The difference isn't better policing. Aside from the fringe issue of organized crime, most bike theft is associated with addicts trying to make a quick buck to buy drugs and we already know police isn't the answer to reducing drug addiction.
A better long-term solution would be to reduce the need for policing by mending the socioeconomic conditions that result in bike theft. Rampant bike theft isn't a global issue and is actually less of an issue in some countries that have a lot more bikes on the streets per person than any city in the US does. The difference isn't better policing. Aside from the fringe issue of organized crime, most bike theft is associated with addicts trying to make a quick buck to buy drugs and we already know police isn't the answer to reducing drug addiction.