Um, the police already know all of this. If they use this information, they are not just going to rock up to court with (purportedly) your public transaction history and a subpoena showing that you got a pizza delivered using bitcoins and get a conviction.

They're going to use it to get a warrant to search your house.

And yeah, this trawler like approach will not catch everybody. But it could score a lot of convictions very quickly.