The main possible problems are twofold:
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.