My point is that as payments become more and more digital then we must be wary of what that means in terms of data mining and things like that.
When you report a cash theft, the police don't go looking for the serial numbers of the notes (usually). They look for other evidence, like your house being broken into and the burglar leaving evidence behind. Imagine you've created a situation where there is no evidence that you live in your own house!
Yeah, there would be slim chances of recovering the stolen money, but that already is the case with cash, given a smart enough robber. The right way to tackle that problem is not to make the stolen goods easy to track, but to have preventive measures. In Bitcoin's case, these measures would be good security practices.