The whole public transaction log makes it easy to trace every transaction made by a person, especially in widespread use. If you want to stop bitcoin, making using it a crime and then set up false flag merchants (or give immunity to merchants for cooperating) and it becomes trivial to track individuals.

And as for p2p communication, again, easy to find and charge anybody participating in the network.

Alternatively, don't make bitcoin illegal, just heavily use it to track and arrest people using it for already illegal things, preferably in a shock and awe way where you make a big show of arresting a bunch of criminals at once and then brag in the media about how bitcoin made it all possible.

Bitcoin is terrible at privacy unless you're trying really hard to conceal your identity.