1. The purpose of DRM is to prevent people from copying content while allowing people to view that content,
2. You can't hide something from someone while showing it to them,
3. And in any case widespread copyright violations (e.g. movies on file sharing sites) often come from sources that aren't encrypted in the first place, e.g. leaks from studios.
It turns out that this argument is fundamentally flawed. Usually the arguments from pro-DRM people are that #2 and #3 are false. But no, those are true. The problem is #1 is false.
The purpose of DRM is not to prevent copyright violations.
The purpose of DRM is to give content providers leverage against creators of playback devices.
Content providers have leverage against content distributors, because distributors can't legally distribute copyrighted content without the permission of the content's creators. But if that was the only leverage content producers had, what would happen is that users would obtain their content from those content distributors, and then use third-party content playback systems to read it, letting them do so in whatever manner they wanted.
Here are some examples:
A. Paramount make a movie. A DVD store buys the rights to distribute this movie from Paramount, and sells DVDs. You buy the DVD, and want to play it. Paramount want you to sit through some ads, so they tell the DVD store to put some ads on the DVD labeled as "unskippable".
Without DRM, you take the DVD and stick it into a DVD player that ignores "unskippable" labels, and jump straight to the movie.
With DRM, there is no licensed player that can do this, because to create the player you need to get permission from Paramount -- or rather, a licensing agent created and supported by content companies, DVD-CCA -- otherwise, you are violating some set of patents, anti-circumvention laws, or both.
B. Columbia make a movie. Netflix buys the rights to distribute this movie from Columbia, and sells access to the bits of the movie to users online. You get a Netflix subscription. Columbia want you to pay more if you want to watch it simultaneously on your TV and your phone, so they require that Netflix prevent you from doing this.
Now. You are watching the movie upstairs with your family, and you hear your cat meowing at the door downstairs.
Without DRM, you don't have to use Netflix's software, so maybe just pass the feed to some multiplexing software, which means that you can just pick up your phone, tell it to stream the same movie, continue watching it while you walk downstairs to open the door for the cat, come back upstairs, and turn your phone off, and nobody else has been inconvenienced and you haven't missed anything.
With DRM, you have to use Netflix's software, so you have to play by their rules. There is no licensed software that will let you multiplex the stream. You could watch it on your phone, but then your family misses out. They could keep watching, but then you miss out. Nobody is allowed to write software that does anything Columbia don't want you to do. Columbia want the option to charge you more when you go to let your cat in, even if they don't actually make it possible yet.
C. Fox make a movie. Apple buys the rights to sell it on iTunes. You buy it from iTunes. You want to watch it on your phone. Fox want you to buy the movie again if you use anything not made by Apple.
Without DRM, you just transfer it to your phone and watch it, since the player on any phone, whether made by Apple or anyone else, can read the video file.
With DRM, only Apple can provide a licensed player for the file. If you're using any phone other than an iPhone, you cannot watch it, because nobody else has been allowed to write software that decrypts the media files sold by Apple.
In all three cases, nobody has been stopped from violating a copyright. All three movies are probably available on file sharing sites. The only people who are stopped from doing anything are the player providers -- they are forced to provide a user experience that, rather than being optimised for the users, puts potential future revenues first (forcing people to play ads, keeping the door open to charging more for more features later, building artificial obsolescence into content so that if you change ecosystem, you have to purchase the content again).
Arguing that DRM doesn't work is, it turns out, missing the point. DRM is working really well in the video and book space. Sure, the DRM systems have all been broken, but that doesn't matter to the DRM proponents. Licensed DVD players still enforce the restrictions. Mass market providers can't create unlicensed DVD players, so they remain a black or gray market curiosity. DRM failed in the music space not because DRM is doomed, but because the content providers sold their digital content without DRM, and thus enabled all kinds of players they didn't expect (such as "MP3" players). Had CDs been encrypted, iPods would not have been able to read their content, because the content providers would have been able to use their DRM contracts as leverage to prevent it.
DRM's purpose is to give content providers control over software and hardware providers, and it is satisfying that purpose well.
As a corollary to this, look at the companies who are pushing for DRM. Of the ones who would have to implement the DRM, they are all companies over which the content providers already, without DRM, have leverage: the companies that both license content from the content providers and create software or hardware players. Because they license content, the content providers already have leverage against them: they can essentially require them to be pro-DRM if they want the content. The people against the DRM are the users, and the player creators who don't license content. In other words, the people over whom the content producers have no leverage.