I agree. I think you probably spent more on the tires than the whole bike is really worth. However, the point is the same. If you can actually get a bike thief prosecuted, which I doubt, I'd fully support you following up on it.

The problem is that the person in possession of the bike now can claim to have purchased the bike at a thrift store, from a friend/stranger etc. At best you'll get the bike back but it would be impossible to prove that the bike was actually "stolen" and there is no proof that the person in possession of it is the person that actually stole it in the first place. Basically it will bog down into a he said/she said. Which after all is essentially what police work is anyway. Which is why DAs prosecute so few actual cases. They want to win at trial.