Sure DRM is bad, but you can't tell people not to build things a priori like that, and DRM will be built because the content studios demand it, and the studios hold the content which everyone wants. The EFF greatly overestimates the amount of influence browser makers have. No amount of technical pressure will make an ounce of difference, because browser makers have literally no leverage on rights holders. If the streaming technology isn't available, then the studios will simply choose not to stream it, and whoever builds it first will have a huge market advantage.
Fighting EME not only is ineffectual, it harms open web standards by giving legs to completely proprietary solutions like Flash and Silverlight. The bottom line is that EME is a cleaner solution which compromises in a way that will make open standards more relevant going forward rather than taking an ideological position that will undermine the utility of open standards in the marketplace.
Instead of attempting to fight a self-harming losing battle, I wish the EFF would focus on the real problem which is the DMCA's overreach. Studios should feel free to build whatever DRM schemes they want, just like the people should be free to circumvent those measures for content they have legally purchased. Copyright law is sufficient to balance individual and studios' rights across a diversity of scenarios with getting a technical quagmire that benefits no one.