It's quite different because in case of you downloading and especially sharing pirate content, you are actually doing something wrong. While I agree that it's impossible to punish the majority of the people sharing pirate content, it does happen occasionally. It's not for nothing that a lot people now are using either VPN's or dedicated servers to distract attention away from their own download location. It's basically a case of better safe than sorry. On top of that, if you download stuff from your home computer, your IP is publicly known, and thus you can be held responsible for your actions, while if you transact with Bitcoin, only the IP of the first node is basically your taint. In most lightweight clients you can choose the node you connect to or you can even manually connect to a node of your choice. Authorities can't do anything about it.
Do not get me wrong I'm not trying to justify piracy in any way or form, it's just an example to show how difficult it is to deal with a problem at a decentralized level, governments are very good at dealing with centralized opponents of any kind, but they are terrible at dealing with movements without a visible head and that do not depend on it to organize itself, which is why file sharing is still very popular even in this day and age where governments have such tremendous powers of spying over the population, which means that they have almost no hope of stopping bitcoin no matter what they do.
You don't have to control Bitcoin itself, you only have to control the fiat gateways, which is already in the realm of what the government does. Fiat gateways are exchanges that will convert crypto for fiat or vice versa. Because these exchanges operate as quasi-financial institutions, which are already very well-regulated, it's not difficult at all to expand current legal requirements to crypto exchanges. All (or at least most) of the major exchanges are already compliant with applicable rules and regulations or seeking to be, and what's more is that users will increasingly demand this so that there is more confidence that any wrongdoing by the exchanges will be accountable. There have been far too many scams and collapses that have happened without consequence to the bad actors, and everyone wants the confidence that the exchanges aren't run by idiots or charlatans. If the industry was capable of policing itself, it would have by now.
There's just one point which you don't take into account but which makes things a little more complicated for "the government". The point is that there is no single government (conspiracy theories aside), and it is not just about stating there are over 200 of them presently. Yes, only a few matter, live up and amount to being really independent, but even one is more than enough. The contradictions between these governments are so irreconcilable that all of them will be happy to use Bitcoin or whatever if it suits their needs in opposing the rest of the pack. This includes, but is definitely not limited to, fiat gateways and exchanges in question.
I don't know if you are familiar with the events surrounding taking down btc-e by the FBI, but the end result is that the latter failed pathetically at reaching their ends. And it is likely the most powerful law enforcement agency of the most powerful and stubborn government in the world hellbent on punishing everyone to dare them which couldn't take down just one exchange. So it doesn't look like it is actually "in the realm of what the government does" when it comes to real world.
In short, there is light at the end of the tunnel.
My point didn't come across, so let me rephrase. The government already controls traditional fiat gateways, which are points at which you exchange fiat for electronic cash. Banks, currency exchanges, money transfer businesses, brokerages, stock exchanges: all regulated by the government. You cannot move large amounts of money through any traditional fiat gateway anonymously because they are so tightly regulated. These same choke points exist for crypto. You don't have to control crypto, you just have to pass regulations outlawing all the traditional gateways from dealing in it, and because the people running the businesses can't do so anonymously, violations of the law will be easy to prosecute. That won't kill crypto completely, but it will greatly reduce its use and value by driving it deep underground and stall adoption for normal people who aren't interested in becoming criminals by using it and deal with the hassle of trying to avoid detection in converting fiat back and forth. There would essentially be no incentive to any longer except for criminals at that point.