but whether the police would be able to do anything about it is another matter.
I'd stick an "immediately" in there. In 5-10 years, all police may have computing resources for deep blockchain analysis, and be able to "clear up" old theft and fraud reports with a couple of mouse clicks. Should the jurisdiction they are in be letting the department keep a proportion of the fine or court award against the thief or fraudster, you become a cash cow to be milked.
This will probably be much more difficult they you imply, especially for smaller amounts.
It is very difficult to know when a transaction is sending bitcoin to another person or just a transfer to yourself (plus if you properly use change addresses, almost every transaction will include one transfer to yourself).
Even if stolen bitcoin is transferred directly to an exchange, it is possible that the exchange could go out of business sometime between now and 10 years from now, leaving behind no records, so even if it is determined that an address associated with stolen bitcoin belongs to a specific exchange (who verified someone's identity) it may not be possible to determine who exactly was behind the transaction