It'd make no sense to let people roll their own browsers that circumvent DRM.
What exactly do you think will prevent them from building their already-existing in-house DRM (three different systems, note!) into their own browsers?
Would that somehow lead to Hacker News or Facebook encrypting their site's source code with that DRM? I sort of doubt it. They could do that now with Flash if they wanted to, but no one thinks Flash websites are a good idea.
1) EME as currently proposed is video only, but will the W3C try to do the same for images? For text? There are certainly constituencies who would live simple turnkey DRM for those on the web. And they don't do it in Flash _precisely_ because Flash websites are not a good idea.
2) If the above happens, there is no incentive for Netflix, say, to try come up with a setup that works with open-source browsers and still satisfies the rightsholders for the content they distribute. If people complain they'll just be told the spec says browsers need to implement DRM, and if that means no open-source browsers tough luck.
You're also assuming that consumers give a crap about DRM. They generally don't, if they get the content they want is available at a good price (i.e. mostly free w/ advertising if it's low-engagement, or at cost if it's high-engagement), and good a user experience (i.e. I can consume it on my chosen device platform, in my chosen setting, without having to stand on my head).
DRM became a detractor for consumers in the music industry because they went to war with their own customers. Music has a multi-decade long culture of sharing and trading. Then the industry retroactively tries to state that all of this is illegal. You couldn't easily copy purchased files across devices due to their paranoia. Even iPods could only be sync'd to one library at a time (part of their settlement with Apple in the early 00's). They even tried to claim CD ripping was illegal (that didn't fly). This is why Apple advocated to get DRM removed altogether from iTunes and eventually won - it was just a crappy experience all around.
The TV/movie industry thus far has avoided the fate of the music industry through a mix of low-barrier access to content within the US (Hulu, iTunes, Netflix TV station websites, etc.) and DRM to erect some exclusionary barriers to the content. DRM in this sector is more like a horse race that doesn't quell piracy but keeps it at least somewhat inconvenient. They also didn't go to war with their customers, and were more selective of how they chose to use legal avenues.
I don't foresee death in their future, just winner-take-all competition if they don't keep up with what their customers want.
Ultimately, the nature of most information goods being non-excludable is changing the game in ALL industries that make and sell information from one of distributing the information to a hybrid market-gift-economy. You can have previews, clips, etc. to experience my stuff, perhaps even stream it for free for a limited time, but to get the best overall experience, they'll gate the access... i.e. you can't have my stuff unless you line up and pay a ticket. This is even how RedHat works (you need to pay to get into RHN, or their cloud... which are the best experiences of maintaining a RedHat server, even though the software itself is free).
Or they focus on something that is excludable: a consumer's time and attention... i.e. free TV streaming, or Facebook surfing time. And make money on the content with advertising.
It's not bad or good for consumers, at best, it's about the same. It's very simple, studios will not allow you to rent their movies without DRM. Netflix will not be able to function without DRM. Neither can steam. It's not up to them, it's up to the content providers, not companies like Netflix.
Is it stupid? Yes. My high school teacher, with no technical knowledge what so ever had a way to brake almost any video DRM. He would play the video on his TV, and record the image with his HD Cam. Stupid? Yes. Effective? Also yes.
The point is, as long as its a plugin type of architecture, not part of the browser binary, what's the big deal. How is it different from Flash or Silverlight?
Oh, and to everyone that proclaims that DRM is bad. Many of you are developers for startups. Is your startup all open source? Why not? Isn't compiling code or running it only on your servers just another type of DRM? Ask your self, would you have a job if your company was forced to share all the code you write? All of it, even the stuff that you write from scratch and only run on your servers.
I think many people hate DRM because of how bad it's implemented, not because of the fact that its there in the first place. Well implemented DRM should be completely transparent to the end user who paid for the content. Steam and Netflix do a pretty good job of it.